YES Problem: +(0(),0()) -> 0() +(0(),1()) -> 1() +(0(),2()) -> 2() +(0(),3()) -> 3() +(0(),4()) -> 4() +(0(),5()) -> 5() +(0(),6()) -> 6() +(0(),7()) -> 7() +(0(),8()) -> 8() +(0(),9()) -> 9() +(1(),0()) -> 1() +(1(),1()) -> 2() +(1(),2()) -> 3() +(1(),3()) -> 4() +(1(),4()) -> 5() +(1(),5()) -> 6() +(1(),6()) -> 7() +(1(),7()) -> 8() +(1(),8()) -> 9() +(1(),9()) -> c(1(),0()) +(2(),0()) -> 2() +(2(),1()) -> 3() +(2(),2()) -> 4() +(2(),3()) -> 5() +(2(),4()) -> 6() +(2(),5()) -> 7() +(2(),6()) -> 8() +(2(),7()) -> 9() +(2(),8()) -> c(1(),0()) +(2(),9()) -> c(1(),1()) +(3(),0()) -> 3() +(3(),1()) -> 4() +(3(),2()) -> 5() +(3(),3()) -> 6() +(3(),4()) -> 7() +(3(),5()) -> 8() +(3(),6()) -> 9() +(3(),7()) -> c(1(),0()) +(3(),8()) -> c(1(),1()) +(3(),9()) -> c(1(),2()) +(4(),0()) -> 4() +(4(),1()) -> 5() +(4(),2()) -> 6() +(4(),3()) -> 7() +(4(),4()) -> 8() +(4(),5()) -> 9() +(4(),6()) -> c(1(),0()) +(4(),7()) -> c(1(),1()) +(4(),8()) -> c(1(),2()) +(4(),9()) -> c(1(),3()) +(5(),0()) -> 5() +(5(),1()) -> 6() +(5(),2()) -> 7() +(5(),3()) -> 8() +(5(),4()) -> 9() +(5(),5()) -> c(1(),0()) +(5(),6()) -> c(1(),1()) +(5(),7()) -> c(1(),2()) +(5(),8()) -> c(1(),3()) +(5(),9()) -> c(1(),4()) +(6(),0()) -> 6() +(6(),1()) -> 7() +(6(),2()) -> 8() +(6(),3()) -> 9() +(6(),4()) -> c(1(),0()) +(6(),5()) -> c(1(),1()) +(6(),6()) -> c(1(),2()) +(6(),7()) -> c(1(),3()) +(6(),8()) -> c(1(),4()) +(6(),9()) -> c(1(),5()) +(7(),0()) -> 7() +(7(),1()) -> 8() +(7(),2()) -> 9() +(7(),3()) -> c(1(),0()) +(7(),4()) -> c(1(),1()) +(7(),5()) -> c(1(),2()) +(7(),6()) -> c(1(),3()) +(7(),7()) -> c(1(),4()) +(7(),8()) -> c(1(),5()) +(7(),9()) -> c(1(),6()) +(8(),0()) -> 8() +(8(),1()) -> 9() +(8(),2()) -> c(1(),0()) +(8(),3()) -> c(1(),1()) +(8(),4()) -> c(1(),2()) +(8(),5()) -> c(1(),3()) +(8(),6()) -> c(1(),4()) +(8(),7()) -> c(1(),5()) +(8(),8()) -> c(1(),6()) +(8(),9()) -> c(1(),7()) +(9(),0()) -> 9() +(9(),1()) -> c(1(),0()) +(9(),2()) -> c(1(),1()) +(9(),3()) -> c(1(),2()) +(9(),4()) -> c(1(),3()) +(9(),5()) -> c(1(),4()) +(9(),6()) -> c(1(),5()) +(9(),7()) -> c(1(),6()) +(9(),8()) -> c(1(),7()) +(9(),9()) -> c(1(),8()) +(x,c(y,z)) -> c(y,+(x,z)) +(c(x,y),z) -> c(x,+(y,z)) c(0(),x) -> x c(x,c(y,z)) -> c(+(x,y),z) Proof: DP Processor: DPs: +#(1(),9()) -> c#(1(),0()) +#(2(),8()) -> c#(1(),0()) +#(2(),9()) -> c#(1(),1()) +#(3(),7()) -> c#(1(),0()) +#(3(),8()) -> c#(1(),1()) +#(3(),9()) -> c#(1(),2()) +#(4(),6()) -> c#(1(),0()) +#(4(),7()) -> c#(1(),1()) +#(4(),8()) -> c#(1(),2()) +#(4(),9()) -> c#(1(),3()) +#(5(),5()) -> c#(1(),0()) +#(5(),6()) -> c#(1(),1()) +#(5(),7()) -> c#(1(),2()) +#(5(),8()) -> c#(1(),3()) +#(5(),9()) -> c#(1(),4()) +#(6(),4()) -> c#(1(),0()) +#(6(),5()) -> c#(1(),1()) +#(6(),6()) -> c#(1(),2()) +#(6(),7()) -> c#(1(),3()) +#(6(),8()) -> c#(1(),4()) +#(6(),9()) -> c#(1(),5()) +#(7(),3()) -> c#(1(),0()) +#(7(),4()) -> c#(1(),1()) +#(7(),5()) -> c#(1(),2()) +#(7(),6()) -> c#(1(),3()) +#(7(),7()) -> c#(1(),4()) +#(7(),8()) -> c#(1(),5()) +#(7(),9()) -> c#(1(),6()) +#(8(),2()) -> c#(1(),0()) +#(8(),3()) -> c#(1(),1()) +#(8(),4()) -> c#(1(),2()) +#(8(),5()) -> c#(1(),3()) +#(8(),6()) -> c#(1(),4()) +#(8(),7()) -> c#(1(),5()) +#(8(),8()) -> c#(1(),6()) +#(8(),9()) -> c#(1(),7()) +#(9(),1()) -> c#(1(),0()) +#(9(),2()) -> c#(1(),1()) +#(9(),3()) -> c#(1(),2()) +#(9(),4()) -> c#(1(),3()) +#(9(),5()) -> c#(1(),4()) +#(9(),6()) -> c#(1(),5()) +#(9(),7()) -> c#(1(),6()) +#(9(),8()) -> c#(1(),7()) +#(9(),9()) -> c#(1(),8()) +#(x,c(y,z)) -> +#(x,z) +#(x,c(y,z)) -> c#(y,+(x,z)) +#(c(x,y),z) -> +#(y,z) +#(c(x,y),z) -> c#(x,+(y,z)) c#(x,c(y,z)) -> +#(x,y) c#(x,c(y,z)) -> c#(+(x,y),z) TRS: +(0(),0()) -> 0() +(0(),1()) -> 1() +(0(),2()) -> 2() +(0(),3()) -> 3() +(0(),4()) -> 4() +(0(),5()) -> 5() +(0(),6()) -> 6() +(0(),7()) -> 7() +(0(),8()) -> 8() +(0(),9()) -> 9() +(1(),0()) -> 1() +(1(),1()) -> 2() +(1(),2()) -> 3() +(1(),3()) -> 4() +(1(),4()) -> 5() +(1(),5()) -> 6() +(1(),6()) -> 7() +(1(),7()) -> 8() +(1(),8()) -> 9() +(1(),9()) -> c(1(),0()) +(2(),0()) -> 2() +(2(),1()) -> 3() +(2(),2()) -> 4() +(2(),3()) -> 5() +(2(),4()) -> 6() +(2(),5()) -> 7() +(2(),6()) -> 8() +(2(),7()) -> 9() +(2(),8()) -> c(1(),0()) +(2(),9()) -> c(1(),1()) +(3(),0()) -> 3() +(3(),1()) -> 4() +(3(),2()) -> 5() +(3(),3()) -> 6() +(3(),4()) -> 7() +(3(),5()) -> 8() +(3(),6()) -> 9() +(3(),7()) -> c(1(),0()) +(3(),8()) -> c(1(),1()) +(3(),9()) -> c(1(),2()) +(4(),0()) -> 4() +(4(),1()) -> 5() +(4(),2()) -> 6() +(4(),3()) -> 7() +(4(),4()) -> 8() +(4(),5()) -> 9() +(4(),6()) -> c(1(),0()) +(4(),7()) -> c(1(),1()) +(4(),8()) -> c(1(),2()) +(4(),9()) -> c(1(),3()) +(5(),0()) -> 5() +(5(),1()) -> 6() +(5(),2()) -> 7() +(5(),3()) -> 8() +(5(),4()) -> 9() +(5(),5()) -> c(1(),0()) +(5(),6()) -> c(1(),1()) +(5(),7()) -> c(1(),2()) +(5(),8()) -> c(1(),3()) +(5(),9()) -> c(1(),4()) +(6(),0()) -> 6() +(6(),1()) -> 7() +(6(),2()) -> 8() +(6(),3()) -> 9() +(6(),4()) -> c(1(),0()) +(6(),5()) -> c(1(),1()) +(6(),6()) -> c(1(),2()) +(6(),7()) -> c(1(),3()) +(6(),8()) -> c(1(),4()) +(6(),9()) -> c(1(),5()) +(7(),0()) -> 7() +(7(),1()) -> 8() +(7(),2()) -> 9() +(7(),3()) -> c(1(),0()) +(7(),4()) -> c(1(),1()) +(7(),5()) -> c(1(),2()) +(7(),6()) -> c(1(),3()) +(7(),7()) -> c(1(),4()) +(7(),8()) -> c(1(),5()) +(7(),9()) -> c(1(),6()) +(8(),0()) -> 8() +(8(),1()) -> 9() +(8(),2()) -> c(1(),0()) +(8(),3()) -> c(1(),1()) +(8(),4()) -> c(1(),2()) +(8(),5()) -> c(1(),3()) +(8(),6()) -> c(1(),4()) +(8(),7()) -> c(1(),5()) +(8(),8()) -> c(1(),6()) +(8(),9()) -> c(1(),7()) +(9(),0()) -> 9() +(9(),1()) -> c(1(),0()) +(9(),2()) -> c(1(),1()) +(9(),3()) -> c(1(),2()) +(9(),4()) -> c(1(),3()) +(9(),5()) -> c(1(),4()) +(9(),6()) -> c(1(),5()) +(9(),7()) -> c(1(),6()) +(9(),8()) -> c(1(),7()) +(9(),9()) -> c(1(),8()) +(x,c(y,z)) -> c(y,+(x,z)) +(c(x,y),z) -> c(x,+(y,z)) c(0(),x) -> x c(x,c(y,z)) -> c(+(x,y),z) TDG Processor: DPs: +#(1(),9()) -> c#(1(),0()) +#(2(),8()) -> c#(1(),0()) +#(2(),9()) -> c#(1(),1()) +#(3(),7()) -> c#(1(),0()) +#(3(),8()) -> c#(1(),1()) +#(3(),9()) -> c#(1(),2()) +#(4(),6()) -> c#(1(),0()) +#(4(),7()) -> c#(1(),1()) +#(4(),8()) -> c#(1(),2()) +#(4(),9()) -> c#(1(),3()) +#(5(),5()) -> c#(1(),0()) +#(5(),6()) -> c#(1(),1()) +#(5(),7()) -> c#(1(),2()) +#(5(),8()) -> c#(1(),3()) +#(5(),9()) -> c#(1(),4()) +#(6(),4()) -> c#(1(),0()) +#(6(),5()) -> c#(1(),1()) +#(6(),6()) -> c#(1(),2()) +#(6(),7()) -> c#(1(),3()) +#(6(),8()) -> c#(1(),4()) +#(6(),9()) -> c#(1(),5()) +#(7(),3()) -> c#(1(),0()) +#(7(),4()) -> c#(1(),1()) +#(7(),5()) -> c#(1(),2()) +#(7(),6()) -> c#(1(),3()) +#(7(),7()) -> c#(1(),4()) +#(7(),8()) -> c#(1(),5()) +#(7(),9()) -> c#(1(),6()) +#(8(),2()) -> c#(1(),0()) +#(8(),3()) -> c#(1(),1()) +#(8(),4()) -> c#(1(),2()) +#(8(),5()) -> c#(1(),3()) +#(8(),6()) -> c#(1(),4()) +#(8(),7()) -> c#(1(),5()) +#(8(),8()) -> c#(1(),6()) +#(8(),9()) -> c#(1(),7()) +#(9(),1()) -> c#(1(),0()) +#(9(),2()) -> c#(1(),1()) +#(9(),3()) -> c#(1(),2()) +#(9(),4()) -> c#(1(),3()) +#(9(),5()) -> c#(1(),4()) +#(9(),6()) -> c#(1(),5()) +#(9(),7()) -> c#(1(),6()) +#(9(),8()) -> c#(1(),7()) +#(9(),9()) -> c#(1(),8()) +#(x,c(y,z)) -> +#(x,z) +#(x,c(y,z)) -> c#(y,+(x,z)) +#(c(x,y),z) -> +#(y,z) +#(c(x,y),z) -> c#(x,+(y,z)) c#(x,c(y,z)) -> +#(x,y) c#(x,c(y,z)) -> c#(+(x,y),z) TRS: +(0(),0()) -> 0() +(0(),1()) -> 1() +(0(),2()) -> 2() +(0(),3()) -> 3() +(0(),4()) -> 4() +(0(),5()) -> 5() +(0(),6()) -> 6() +(0(),7()) -> 7() +(0(),8()) -> 8() +(0(),9()) -> 9() +(1(),0()) -> 1() +(1(),1()) -> 2() +(1(),2()) -> 3() +(1(),3()) -> 4() +(1(),4()) -> 5() +(1(),5()) -> 6() +(1(),6()) -> 7() +(1(),7()) -> 8() +(1(),8()) -> 9() +(1(),9()) -> c(1(),0()) +(2(),0()) -> 2() +(2(),1()) -> 3() +(2(),2()) -> 4() +(2(),3()) -> 5() +(2(),4()) -> 6() +(2(),5()) -> 7() +(2(),6()) -> 8() +(2(),7()) -> 9() +(2(),8()) -> c(1(),0()) +(2(),9()) -> c(1(),1()) +(3(),0()) -> 3() +(3(),1()) -> 4() +(3(),2()) -> 5() +(3(),3()) -> 6() +(3(),4()) -> 7() +(3(),5()) -> 8() +(3(),6()) -> 9() +(3(),7()) -> c(1(),0()) +(3(),8()) -> c(1(),1()) +(3(),9()) -> c(1(),2()) +(4(),0()) -> 4() +(4(),1()) -> 5() +(4(),2()) -> 6() +(4(),3()) -> 7() +(4(),4()) -> 8() +(4(),5()) -> 9() +(4(),6()) -> c(1(),0()) +(4(),7()) -> c(1(),1()) +(4(),8()) -> c(1(),2()) +(4(),9()) -> c(1(),3()) +(5(),0()) -> 5() +(5(),1()) -> 6() +(5(),2()) -> 7() +(5(),3()) -> 8() +(5(),4()) -> 9() +(5(),5()) -> c(1(),0()) +(5(),6()) -> c(1(),1()) +(5(),7()) -> c(1(),2()) +(5(),8()) -> c(1(),3()) +(5(),9()) -> c(1(),4()) +(6(),0()) -> 6() +(6(),1()) -> 7() +(6(),2()) -> 8() +(6(),3()) -> 9() +(6(),4()) -> c(1(),0()) +(6(),5()) -> c(1(),1()) +(6(),6()) -> c(1(),2()) +(6(),7()) -> c(1(),3()) +(6(),8()) -> c(1(),4()) +(6(),9()) -> c(1(),5()) +(7(),0()) -> 7() +(7(),1()) -> 8() +(7(),2()) -> 9() +(7(),3()) -> c(1(),0()) +(7(),4()) -> c(1(),1()) +(7(),5()) -> c(1(),2()) +(7(),6()) -> c(1(),3()) +(7(),7()) -> c(1(),4()) +(7(),8()) -> c(1(),5()) +(7(),9()) -> c(1(),6()) +(8(),0()) -> 8() +(8(),1()) -> 9() +(8(),2()) -> c(1(),0()) +(8(),3()) -> c(1(),1()) +(8(),4()) -> c(1(),2()) +(8(),5()) -> c(1(),3()) +(8(),6()) -> c(1(),4()) +(8(),7()) -> c(1(),5()) +(8(),8()) -> c(1(),6()) +(8(),9()) -> c(1(),7()) +(9(),0()) -> 9() +(9(),1()) -> c(1(),0()) +(9(),2()) -> c(1(),1()) +(9(),3()) -> c(1(),2()) +(9(),4()) -> c(1(),3()) +(9(),5()) -> c(1(),4()) +(9(),6()) -> c(1(),5()) +(9(),7()) -> c(1(),6()) +(9(),8()) -> c(1(),7()) +(9(),9()) -> c(1(),8()) +(x,c(y,z)) -> c(y,+(x,z)) +(c(x,y),z) -> c(x,+(y,z)) c(0(),x) -> x c(x,c(y,z)) -> c(+(x,y),z) graph: c#(x,c(y,z)) -> c#(+(x,y),z) -> c#(x,c(y,z)) -> c#(+(x,y),z) c#(x,c(y,z)) -> c#(+(x,y),z) -> c#(x,c(y,z)) -> +#(x,y) c#(x,c(y,z)) -> +#(x,y) -> +#(c(x,y),z) -> c#(x,+(y,z)) c#(x,c(y,z)) -> +#(x,y) -> +#(c(x,y),z) -> +#(y,z) c#(x,c(y,z)) -> +#(x,y) -> +#(x,c(y,z)) -> c#(y,+(x,z)) c#(x,c(y,z)) -> +#(x,y) -> +#(x,c(y,z)) -> +#(x,z) c#(x,c(y,z)) -> +#(x,y) -> +#(9(),9()) -> c#(1(),8()) c#(x,c(y,z)) -> +#(x,y) -> +#(9(),8()) -> c#(1(),7()) c#(x,c(y,z)) -> +#(x,y) -> +#(9(),7()) -> c#(1(),6()) c#(x,c(y,z)) -> +#(x,y) -> +#(9(),6()) -> c#(1(),5()) c#(x,c(y,z)) -> +#(x,y) -> +#(9(),5()) -> c#(1(),4()) c#(x,c(y,z)) -> +#(x,y) -> +#(9(),4()) -> c#(1(),3()) c#(x,c(y,z)) -> +#(x,y) -> +#(9(),3()) -> c#(1(),2()) c#(x,c(y,z)) -> +#(x,y) -> +#(9(),2()) -> c#(1(),1()) c#(x,c(y,z)) -> +#(x,y) -> +#(9(),1()) -> c#(1(),0()) c#(x,c(y,z)) -> +#(x,y) -> +#(8(),9()) -> c#(1(),7()) c#(x,c(y,z)) -> +#(x,y) -> +#(8(),8()) -> c#(1(),6()) c#(x,c(y,z)) -> +#(x,y) -> +#(8(),7()) -> c#(1(),5()) c#(x,c(y,z)) -> +#(x,y) -> +#(8(),6()) -> c#(1(),4()) c#(x,c(y,z)) -> +#(x,y) -> +#(8(),5()) -> c#(1(),3()) c#(x,c(y,z)) -> +#(x,y) -> +#(8(),4()) -> c#(1(),2()) c#(x,c(y,z)) -> +#(x,y) -> +#(8(),3()) -> c#(1(),1()) c#(x,c(y,z)) -> +#(x,y) -> +#(8(),2()) -> c#(1(),0()) c#(x,c(y,z)) -> +#(x,y) -> +#(7(),9()) -> c#(1(),6()) c#(x,c(y,z)) -> +#(x,y) -> +#(7(),8()) -> c#(1(),5()) c#(x,c(y,z)) -> +#(x,y) -> +#(7(),7()) -> c#(1(),4()) c#(x,c(y,z)) -> +#(x,y) -> +#(7(),6()) -> c#(1(),3()) c#(x,c(y,z)) -> +#(x,y) -> +#(7(),5()) -> c#(1(),2()) c#(x,c(y,z)) -> +#(x,y) -> +#(7(),4()) -> c#(1(),1()) c#(x,c(y,z)) -> +#(x,y) -> +#(7(),3()) -> c#(1(),0()) c#(x,c(y,z)) -> +#(x,y) -> +#(6(),9()) -> c#(1(),5()) c#(x,c(y,z)) -> +#(x,y) -> +#(6(),8()) -> c#(1(),4()) c#(x,c(y,z)) -> +#(x,y) -> +#(6(),7()) -> c#(1(),3()) c#(x,c(y,z)) -> +#(x,y) -> +#(6(),6()) -> c#(1(),2()) c#(x,c(y,z)) -> +#(x,y) -> +#(6(),5()) -> c#(1(),1()) c#(x,c(y,z)) -> +#(x,y) -> +#(6(),4()) -> c#(1(),0()) c#(x,c(y,z)) -> +#(x,y) -> +#(5(),9()) -> c#(1(),4()) c#(x,c(y,z)) -> +#(x,y) -> +#(5(),8()) -> c#(1(),3()) c#(x,c(y,z)) -> +#(x,y) -> +#(5(),7()) -> c#(1(),2()) c#(x,c(y,z)) -> +#(x,y) -> +#(5(),6()) -> c#(1(),1()) c#(x,c(y,z)) -> +#(x,y) -> +#(5(),5()) -> c#(1(),0()) c#(x,c(y,z)) -> +#(x,y) -> +#(4(),9()) -> c#(1(),3()) c#(x,c(y,z)) -> +#(x,y) -> +#(4(),8()) -> c#(1(),2()) c#(x,c(y,z)) -> +#(x,y) -> +#(4(),7()) -> c#(1(),1()) c#(x,c(y,z)) -> +#(x,y) -> +#(4(),6()) -> c#(1(),0()) c#(x,c(y,z)) -> +#(x,y) -> +#(3(),9()) -> c#(1(),2()) c#(x,c(y,z)) -> +#(x,y) -> +#(3(),8()) -> c#(1(),1()) c#(x,c(y,z)) -> +#(x,y) -> +#(3(),7()) -> c#(1(),0()) c#(x,c(y,z)) -> +#(x,y) -> +#(2(),9()) -> c#(1(),1()) c#(x,c(y,z)) -> +#(x,y) -> +#(2(),8()) -> c#(1(),0()) c#(x,c(y,z)) -> +#(x,y) -> +#(1(),9()) -> c#(1(),0()) +#(c(x,y),z) -> c#(x,+(y,z)) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(c(x,y),z) -> c#(x,+(y,z)) -> c#(x,c(y,z)) -> +#(x,y) +#(c(x,y),z) -> +#(y,z) -> +#(c(x,y),z) -> c#(x,+(y,z)) +#(c(x,y),z) -> +#(y,z) -> +#(c(x,y),z) -> +#(y,z) +#(c(x,y),z) -> +#(y,z) -> +#(x,c(y,z)) -> c#(y,+(x,z)) +#(c(x,y),z) -> +#(y,z) -> +#(x,c(y,z)) -> +#(x,z) +#(c(x,y),z) -> +#(y,z) -> +#(9(),9()) -> c#(1(),8()) +#(c(x,y),z) -> +#(y,z) -> +#(9(),8()) -> c#(1(),7()) +#(c(x,y),z) -> +#(y,z) -> +#(9(),7()) -> c#(1(),6()) +#(c(x,y),z) -> +#(y,z) -> +#(9(),6()) -> c#(1(),5()) +#(c(x,y),z) -> +#(y,z) -> +#(9(),5()) -> c#(1(),4()) +#(c(x,y),z) -> +#(y,z) -> +#(9(),4()) -> c#(1(),3()) +#(c(x,y),z) -> +#(y,z) -> +#(9(),3()) -> c#(1(),2()) +#(c(x,y),z) -> +#(y,z) -> +#(9(),2()) -> c#(1(),1()) +#(c(x,y),z) -> +#(y,z) -> +#(9(),1()) -> c#(1(),0()) +#(c(x,y),z) -> +#(y,z) -> +#(8(),9()) -> c#(1(),7()) +#(c(x,y),z) -> +#(y,z) -> +#(8(),8()) -> c#(1(),6()) +#(c(x,y),z) -> +#(y,z) -> +#(8(),7()) -> c#(1(),5()) +#(c(x,y),z) -> +#(y,z) -> +#(8(),6()) -> c#(1(),4()) +#(c(x,y),z) -> +#(y,z) -> +#(8(),5()) -> c#(1(),3()) +#(c(x,y),z) -> +#(y,z) -> +#(8(),4()) -> c#(1(),2()) +#(c(x,y),z) -> +#(y,z) -> +#(8(),3()) -> c#(1(),1()) +#(c(x,y),z) -> +#(y,z) -> +#(8(),2()) -> c#(1(),0()) +#(c(x,y),z) -> +#(y,z) -> +#(7(),9()) -> c#(1(),6()) +#(c(x,y),z) -> +#(y,z) -> +#(7(),8()) -> c#(1(),5()) +#(c(x,y),z) -> +#(y,z) -> +#(7(),7()) -> c#(1(),4()) +#(c(x,y),z) -> +#(y,z) -> +#(7(),6()) -> c#(1(),3()) +#(c(x,y),z) -> +#(y,z) -> +#(7(),5()) -> c#(1(),2()) +#(c(x,y),z) -> +#(y,z) -> +#(7(),4()) -> c#(1(),1()) +#(c(x,y),z) -> +#(y,z) -> +#(7(),3()) -> c#(1(),0()) +#(c(x,y),z) -> +#(y,z) -> +#(6(),9()) -> c#(1(),5()) +#(c(x,y),z) -> +#(y,z) -> +#(6(),8()) -> c#(1(),4()) +#(c(x,y),z) -> +#(y,z) -> +#(6(),7()) -> c#(1(),3()) +#(c(x,y),z) -> +#(y,z) -> +#(6(),6()) -> c#(1(),2()) +#(c(x,y),z) -> +#(y,z) -> +#(6(),5()) -> c#(1(),1()) +#(c(x,y),z) -> +#(y,z) -> +#(6(),4()) -> c#(1(),0()) +#(c(x,y),z) -> +#(y,z) -> +#(5(),9()) -> c#(1(),4()) +#(c(x,y),z) -> +#(y,z) -> +#(5(),8()) -> c#(1(),3()) +#(c(x,y),z) -> +#(y,z) -> +#(5(),7()) -> c#(1(),2()) +#(c(x,y),z) -> +#(y,z) -> +#(5(),6()) -> c#(1(),1()) +#(c(x,y),z) -> +#(y,z) -> +#(5(),5()) -> c#(1(),0()) +#(c(x,y),z) -> +#(y,z) -> +#(4(),9()) -> c#(1(),3()) +#(c(x,y),z) -> +#(y,z) -> +#(4(),8()) -> c#(1(),2()) +#(c(x,y),z) -> +#(y,z) -> +#(4(),7()) -> c#(1(),1()) +#(c(x,y),z) -> +#(y,z) -> +#(4(),6()) -> c#(1(),0()) +#(c(x,y),z) -> +#(y,z) -> +#(3(),9()) -> c#(1(),2()) +#(c(x,y),z) -> +#(y,z) -> +#(3(),8()) -> c#(1(),1()) +#(c(x,y),z) -> +#(y,z) -> +#(3(),7()) -> c#(1(),0()) +#(c(x,y),z) -> +#(y,z) -> +#(2(),9()) -> c#(1(),1()) +#(c(x,y),z) -> +#(y,z) -> +#(2(),8()) -> c#(1(),0()) +#(c(x,y),z) -> +#(y,z) -> +#(1(),9()) -> c#(1(),0()) +#(9(),9()) -> c#(1(),8()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(9(),9()) -> c#(1(),8()) -> c#(x,c(y,z)) -> +#(x,y) +#(9(),8()) -> c#(1(),7()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(9(),8()) -> c#(1(),7()) -> c#(x,c(y,z)) -> +#(x,y) +#(9(),7()) -> c#(1(),6()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(9(),7()) -> c#(1(),6()) -> c#(x,c(y,z)) -> +#(x,y) +#(9(),6()) -> c#(1(),5()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(9(),6()) -> c#(1(),5()) -> c#(x,c(y,z)) -> +#(x,y) +#(9(),5()) -> c#(1(),4()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(9(),5()) -> c#(1(),4()) -> c#(x,c(y,z)) -> +#(x,y) +#(9(),4()) -> c#(1(),3()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(9(),4()) -> c#(1(),3()) -> c#(x,c(y,z)) -> +#(x,y) +#(9(),3()) -> c#(1(),2()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(9(),3()) -> c#(1(),2()) -> c#(x,c(y,z)) -> +#(x,y) +#(9(),2()) -> c#(1(),1()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(9(),2()) -> c#(1(),1()) -> c#(x,c(y,z)) -> +#(x,y) +#(9(),1()) -> c#(1(),0()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(9(),1()) -> c#(1(),0()) -> c#(x,c(y,z)) -> +#(x,y) +#(8(),9()) -> c#(1(),7()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(8(),9()) -> c#(1(),7()) -> c#(x,c(y,z)) -> +#(x,y) +#(8(),8()) -> c#(1(),6()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(8(),8()) -> c#(1(),6()) -> c#(x,c(y,z)) -> +#(x,y) +#(8(),7()) -> c#(1(),5()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(8(),7()) -> c#(1(),5()) -> c#(x,c(y,z)) -> +#(x,y) +#(8(),6()) -> c#(1(),4()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(8(),6()) -> c#(1(),4()) -> c#(x,c(y,z)) -> +#(x,y) +#(8(),5()) -> c#(1(),3()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(8(),5()) -> c#(1(),3()) -> c#(x,c(y,z)) -> +#(x,y) +#(8(),4()) -> c#(1(),2()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(8(),4()) -> c#(1(),2()) -> c#(x,c(y,z)) -> +#(x,y) +#(8(),3()) -> c#(1(),1()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(8(),3()) -> c#(1(),1()) -> c#(x,c(y,z)) -> +#(x,y) +#(8(),2()) -> c#(1(),0()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(8(),2()) -> c#(1(),0()) -> c#(x,c(y,z)) -> +#(x,y) +#(7(),9()) -> c#(1(),6()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(7(),9()) -> c#(1(),6()) -> c#(x,c(y,z)) -> +#(x,y) +#(7(),8()) -> c#(1(),5()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(7(),8()) -> c#(1(),5()) -> c#(x,c(y,z)) -> +#(x,y) +#(7(),7()) -> c#(1(),4()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(7(),7()) -> c#(1(),4()) -> c#(x,c(y,z)) -> +#(x,y) +#(7(),6()) -> c#(1(),3()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(7(),6()) -> c#(1(),3()) -> c#(x,c(y,z)) -> +#(x,y) +#(7(),5()) -> c#(1(),2()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(7(),5()) -> c#(1(),2()) -> c#(x,c(y,z)) -> +#(x,y) +#(7(),4()) -> c#(1(),1()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(7(),4()) -> c#(1(),1()) -> c#(x,c(y,z)) -> +#(x,y) +#(7(),3()) -> c#(1(),0()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(7(),3()) -> c#(1(),0()) -> c#(x,c(y,z)) -> +#(x,y) +#(6(),9()) -> c#(1(),5()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(6(),9()) -> c#(1(),5()) -> c#(x,c(y,z)) -> +#(x,y) +#(6(),8()) -> c#(1(),4()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(6(),8()) -> c#(1(),4()) -> c#(x,c(y,z)) -> +#(x,y) +#(6(),7()) -> c#(1(),3()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(6(),7()) -> c#(1(),3()) -> c#(x,c(y,z)) -> +#(x,y) +#(6(),6()) -> c#(1(),2()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(6(),6()) -> c#(1(),2()) -> c#(x,c(y,z)) -> +#(x,y) +#(6(),5()) -> c#(1(),1()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(6(),5()) -> c#(1(),1()) -> c#(x,c(y,z)) -> +#(x,y) +#(6(),4()) -> c#(1(),0()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(6(),4()) -> c#(1(),0()) -> c#(x,c(y,z)) -> +#(x,y) +#(5(),9()) -> c#(1(),4()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(5(),9()) -> c#(1(),4()) -> c#(x,c(y,z)) -> +#(x,y) +#(5(),8()) -> c#(1(),3()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(5(),8()) -> c#(1(),3()) -> c#(x,c(y,z)) -> +#(x,y) +#(5(),7()) -> c#(1(),2()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(5(),7()) -> c#(1(),2()) -> c#(x,c(y,z)) -> +#(x,y) +#(5(),6()) -> c#(1(),1()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(5(),6()) -> c#(1(),1()) -> c#(x,c(y,z)) -> +#(x,y) +#(5(),5()) -> c#(1(),0()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(5(),5()) -> c#(1(),0()) -> c#(x,c(y,z)) -> +#(x,y) +#(4(),9()) -> c#(1(),3()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(4(),9()) -> c#(1(),3()) -> c#(x,c(y,z)) -> +#(x,y) +#(4(),8()) -> c#(1(),2()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(4(),8()) -> c#(1(),2()) -> c#(x,c(y,z)) -> +#(x,y) +#(4(),7()) -> c#(1(),1()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(4(),7()) -> c#(1(),1()) -> c#(x,c(y,z)) -> +#(x,y) +#(4(),6()) -> c#(1(),0()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(4(),6()) -> c#(1(),0()) -> c#(x,c(y,z)) -> +#(x,y) +#(3(),9()) -> c#(1(),2()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(3(),9()) -> c#(1(),2()) -> c#(x,c(y,z)) -> +#(x,y) +#(3(),8()) -> c#(1(),1()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(3(),8()) -> c#(1(),1()) -> c#(x,c(y,z)) -> +#(x,y) +#(3(),7()) -> c#(1(),0()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(3(),7()) -> c#(1(),0()) -> c#(x,c(y,z)) -> +#(x,y) +#(2(),9()) -> c#(1(),1()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(2(),9()) -> c#(1(),1()) -> c#(x,c(y,z)) -> +#(x,y) +#(2(),8()) -> c#(1(),0()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(2(),8()) -> c#(1(),0()) -> c#(x,c(y,z)) -> +#(x,y) +#(1(),9()) -> c#(1(),0()) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(1(),9()) -> c#(1(),0()) -> c#(x,c(y,z)) -> +#(x,y) +#(x,c(y,z)) -> c#(y,+(x,z)) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(x,c(y,z)) -> c#(y,+(x,z)) -> c#(x,c(y,z)) -> +#(x,y) +#(x,c(y,z)) -> +#(x,z) -> +#(c(x,y),z) -> c#(x,+(y,z)) +#(x,c(y,z)) -> +#(x,z) -> +#(c(x,y),z) -> +#(y,z) +#(x,c(y,z)) -> +#(x,z) -> +#(x,c(y,z)) -> c#(y,+(x,z)) +#(x,c(y,z)) -> +#(x,z) -> +#(x,c(y,z)) -> +#(x,z) +#(x,c(y,z)) -> +#(x,z) -> +#(9(),9()) -> c#(1(),8()) +#(x,c(y,z)) -> +#(x,z) -> +#(9(),8()) -> c#(1(),7()) +#(x,c(y,z)) -> +#(x,z) -> +#(9(),7()) -> c#(1(),6()) +#(x,c(y,z)) -> +#(x,z) -> +#(9(),6()) -> c#(1(),5()) +#(x,c(y,z)) -> +#(x,z) -> +#(9(),5()) -> c#(1(),4()) +#(x,c(y,z)) -> +#(x,z) -> +#(9(),4()) -> c#(1(),3()) +#(x,c(y,z)) -> +#(x,z) -> +#(9(),3()) -> c#(1(),2()) +#(x,c(y,z)) -> +#(x,z) -> +#(9(),2()) -> c#(1(),1()) +#(x,c(y,z)) -> +#(x,z) -> +#(9(),1()) -> c#(1(),0()) +#(x,c(y,z)) -> +#(x,z) -> +#(8(),9()) -> c#(1(),7()) +#(x,c(y,z)) -> +#(x,z) -> +#(8(),8()) -> c#(1(),6()) +#(x,c(y,z)) -> +#(x,z) -> +#(8(),7()) -> c#(1(),5()) +#(x,c(y,z)) -> +#(x,z) -> +#(8(),6()) -> c#(1(),4()) +#(x,c(y,z)) -> +#(x,z) -> +#(8(),5()) -> c#(1(),3()) +#(x,c(y,z)) -> +#(x,z) -> +#(8(),4()) -> c#(1(),2()) +#(x,c(y,z)) -> +#(x,z) -> +#(8(),3()) -> c#(1(),1()) +#(x,c(y,z)) -> +#(x,z) -> +#(8(),2()) -> c#(1(),0()) +#(x,c(y,z)) -> +#(x,z) -> +#(7(),9()) -> c#(1(),6()) +#(x,c(y,z)) -> +#(x,z) -> +#(7(),8()) -> c#(1(),5()) +#(x,c(y,z)) -> +#(x,z) -> +#(7(),7()) -> c#(1(),4()) +#(x,c(y,z)) -> +#(x,z) -> +#(7(),6()) -> c#(1(),3()) +#(x,c(y,z)) -> +#(x,z) -> +#(7(),5()) -> c#(1(),2()) +#(x,c(y,z)) -> +#(x,z) -> +#(7(),4()) -> c#(1(),1()) +#(x,c(y,z)) -> +#(x,z) -> +#(7(),3()) -> c#(1(),0()) +#(x,c(y,z)) -> +#(x,z) -> +#(6(),9()) -> c#(1(),5()) +#(x,c(y,z)) -> +#(x,z) -> +#(6(),8()) -> c#(1(),4()) +#(x,c(y,z)) -> +#(x,z) -> +#(6(),7()) -> c#(1(),3()) +#(x,c(y,z)) -> +#(x,z) -> +#(6(),6()) -> c#(1(),2()) +#(x,c(y,z)) -> +#(x,z) -> +#(6(),5()) -> c#(1(),1()) +#(x,c(y,z)) -> +#(x,z) -> +#(6(),4()) -> c#(1(),0()) +#(x,c(y,z)) -> +#(x,z) -> +#(5(),9()) -> c#(1(),4()) +#(x,c(y,z)) -> +#(x,z) -> +#(5(),8()) -> c#(1(),3()) +#(x,c(y,z)) -> +#(x,z) -> +#(5(),7()) -> c#(1(),2()) +#(x,c(y,z)) -> +#(x,z) -> +#(5(),6()) -> c#(1(),1()) +#(x,c(y,z)) -> +#(x,z) -> +#(5(),5()) -> c#(1(),0()) +#(x,c(y,z)) -> +#(x,z) -> +#(4(),9()) -> c#(1(),3()) +#(x,c(y,z)) -> +#(x,z) -> +#(4(),8()) -> c#(1(),2()) +#(x,c(y,z)) -> +#(x,z) -> +#(4(),7()) -> c#(1(),1()) +#(x,c(y,z)) -> +#(x,z) -> +#(4(),6()) -> c#(1(),0()) +#(x,c(y,z)) -> +#(x,z) -> +#(3(),9()) -> c#(1(),2()) +#(x,c(y,z)) -> +#(x,z) -> +#(3(),8()) -> c#(1(),1()) +#(x,c(y,z)) -> +#(x,z) -> +#(3(),7()) -> c#(1(),0()) +#(x,c(y,z)) -> +#(x,z) -> +#(2(),9()) -> c#(1(),1()) +#(x,c(y,z)) -> +#(x,z) -> +#(2(),8()) -> c#(1(),0()) +#(x,c(y,z)) -> +#(x,z) -> +#(1(),9()) -> c#(1(),0()) EDG Processor: DPs: +#(1(),9()) -> c#(1(),0()) +#(2(),8()) -> c#(1(),0()) +#(2(),9()) -> c#(1(),1()) +#(3(),7()) -> c#(1(),0()) +#(3(),8()) -> c#(1(),1()) +#(3(),9()) -> c#(1(),2()) +#(4(),6()) -> c#(1(),0()) +#(4(),7()) -> c#(1(),1()) +#(4(),8()) -> c#(1(),2()) +#(4(),9()) -> c#(1(),3()) +#(5(),5()) -> c#(1(),0()) +#(5(),6()) -> c#(1(),1()) +#(5(),7()) -> c#(1(),2()) +#(5(),8()) -> c#(1(),3()) +#(5(),9()) -> c#(1(),4()) +#(6(),4()) -> c#(1(),0()) +#(6(),5()) -> c#(1(),1()) +#(6(),6()) -> c#(1(),2()) +#(6(),7()) -> c#(1(),3()) +#(6(),8()) -> c#(1(),4()) +#(6(),9()) -> c#(1(),5()) +#(7(),3()) -> c#(1(),0()) +#(7(),4()) -> c#(1(),1()) +#(7(),5()) -> c#(1(),2()) +#(7(),6()) -> c#(1(),3()) +#(7(),7()) -> c#(1(),4()) +#(7(),8()) -> c#(1(),5()) +#(7(),9()) -> c#(1(),6()) +#(8(),2()) -> c#(1(),0()) +#(8(),3()) -> c#(1(),1()) +#(8(),4()) -> c#(1(),2()) +#(8(),5()) -> c#(1(),3()) +#(8(),6()) -> c#(1(),4()) +#(8(),7()) -> c#(1(),5()) +#(8(),8()) -> c#(1(),6()) +#(8(),9()) -> c#(1(),7()) +#(9(),1()) -> c#(1(),0()) +#(9(),2()) -> c#(1(),1()) +#(9(),3()) -> c#(1(),2()) +#(9(),4()) -> c#(1(),3()) +#(9(),5()) -> c#(1(),4()) +#(9(),6()) -> c#(1(),5()) +#(9(),7()) -> c#(1(),6()) +#(9(),8()) -> c#(1(),7()) +#(9(),9()) -> c#(1(),8()) +#(x,c(y,z)) -> +#(x,z) +#(x,c(y,z)) -> c#(y,+(x,z)) +#(c(x,y),z) -> +#(y,z) +#(c(x,y),z) -> c#(x,+(y,z)) c#(x,c(y,z)) -> +#(x,y) c#(x,c(y,z)) -> c#(+(x,y),z) TRS: +(0(),0()) -> 0() +(0(),1()) -> 1() +(0(),2()) -> 2() +(0(),3()) -> 3() +(0(),4()) -> 4() +(0(),5()) -> 5() +(0(),6()) -> 6() +(0(),7()) -> 7() +(0(),8()) -> 8() +(0(),9()) -> 9() +(1(),0()) -> 1() +(1(),1()) -> 2() +(1(),2()) -> 3() +(1(),3()) -> 4() +(1(),4()) -> 5() +(1(),5()) -> 6() +(1(),6()) -> 7() +(1(),7()) -> 8() +(1(),8()) -> 9() +(1(),9()) -> c(1(),0()) +(2(),0()) -> 2() +(2(),1()) -> 3() +(2(),2()) -> 4() +(2(),3()) -> 5() +(2(),4()) -> 6() +(2(),5()) -> 7() +(2(),6()) -> 8() +(2(),7()) -> 9() +(2(),8()) -> c(1(),0()) +(2(),9()) -> c(1(),1()) +(3(),0()) -> 3() +(3(),1()) -> 4() +(3(),2()) -> 5() +(3(),3()) -> 6() +(3(),4()) -> 7() +(3(),5()) -> 8() +(3(),6()) -> 9() +(3(),7()) -> c(1(),0()) +(3(),8()) -> c(1(),1()) +(3(),9()) -> c(1(),2()) +(4(),0()) -> 4() +(4(),1()) -> 5() +(4(),2()) -> 6() +(4(),3()) -> 7() +(4(),4()) -> 8() +(4(),5()) -> 9() +(4(),6()) -> c(1(),0()) +(4(),7()) -> c(1(),1()) +(4(),8()) -> c(1(),2()) +(4(),9()) -> c(1(),3()) +(5(),0()) -> 5() +(5(),1()) -> 6() +(5(),2()) -> 7() +(5(),3()) -> 8() +(5(),4()) -> 9() +(5(),5()) -> c(1(),0()) +(5(),6()) -> c(1(),1()) +(5(),7()) -> c(1(),2()) +(5(),8()) -> c(1(),3()) +(5(),9()) -> c(1(),4()) +(6(),0()) -> 6() +(6(),1()) -> 7() +(6(),2()) -> 8() +(6(),3()) -> 9() +(6(),4()) -> c(1(),0()) +(6(),5()) -> c(1(),1()) +(6(),6()) -> c(1(),2()) +(6(),7()) -> c(1(),3()) +(6(),8()) -> c(1(),4()) +(6(),9()) -> c(1(),5()) +(7(),0()) -> 7() +(7(),1()) -> 8() +(7(),2()) -> 9() +(7(),3()) -> c(1(),0()) +(7(),4()) -> c(1(),1()) +(7(),5()) -> c(1(),2()) +(7(),6()) -> c(1(),3()) +(7(),7()) -> c(1(),4()) +(7(),8()) -> c(1(),5()) +(7(),9()) -> c(1(),6()) +(8(),0()) -> 8() +(8(),1()) -> 9() +(8(),2()) -> c(1(),0()) +(8(),3()) -> c(1(),1()) +(8(),4()) -> c(1(),2()) +(8(),5()) -> c(1(),3()) +(8(),6()) -> c(1(),4()) +(8(),7()) -> c(1(),5()) +(8(),8()) -> c(1(),6()) +(8(),9()) -> c(1(),7()) +(9(),0()) -> 9() +(9(),1()) -> c(1(),0()) +(9(),2()) -> c(1(),1()) +(9(),3()) -> c(1(),2()) +(9(),4()) -> c(1(),3()) +(9(),5()) -> c(1(),4()) +(9(),6()) -> c(1(),5()) +(9(),7()) -> c(1(),6()) +(9(),8()) -> c(1(),7()) +(9(),9()) -> c(1(),8()) +(x,c(y,z)) -> c(y,+(x,z)) +(c(x,y),z) -> c(x,+(y,z)) c(0(),x) -> x c(x,c(y,z)) -> c(+(x,y),z) graph: c#(x,c(y,z)) -> c#(+(x,y),z) -> c#(x,c(y,z)) -> +#(x,y) c#(x,c(y,z)) -> c#(+(x,y),z) -> c#(x,c(y,z)) -> c#(+(x,y),z) c#(x,c(y,z)) -> +#(x,y) -> +#(1(),9()) -> c#(1(),0()) c#(x,c(y,z)) -> +#(x,y) -> +#(2(),8()) -> c#(1(),0()) c#(x,c(y,z)) -> +#(x,y) -> +#(2(),9()) -> c#(1(),1()) c#(x,c(y,z)) -> +#(x,y) -> +#(3(),7()) -> c#(1(),0()) c#(x,c(y,z)) -> +#(x,y) -> +#(3(),8()) -> c#(1(),1()) c#(x,c(y,z)) -> +#(x,y) -> +#(3(),9()) -> c#(1(),2()) c#(x,c(y,z)) -> +#(x,y) -> +#(4(),6()) -> c#(1(),0()) c#(x,c(y,z)) -> +#(x,y) -> +#(4(),7()) -> c#(1(),1()) c#(x,c(y,z)) -> +#(x,y) -> +#(4(),8()) -> c#(1(),2()) c#(x,c(y,z)) -> +#(x,y) -> +#(4(),9()) -> c#(1(),3()) c#(x,c(y,z)) -> +#(x,y) -> +#(5(),5()) -> c#(1(),0()) c#(x,c(y,z)) -> +#(x,y) -> +#(5(),6()) -> c#(1(),1()) c#(x,c(y,z)) -> +#(x,y) -> +#(5(),7()) -> c#(1(),2()) c#(x,c(y,z)) -> +#(x,y) -> +#(5(),8()) -> c#(1(),3()) c#(x,c(y,z)) -> +#(x,y) -> +#(5(),9()) -> c#(1(),4()) c#(x,c(y,z)) -> +#(x,y) -> +#(6(),4()) -> c#(1(),0()) c#(x,c(y,z)) -> +#(x,y) -> +#(6(),5()) -> c#(1(),1()) c#(x,c(y,z)) -> +#(x,y) -> +#(6(),6()) -> c#(1(),2()) c#(x,c(y,z)) -> +#(x,y) -> +#(6(),7()) -> c#(1(),3()) c#(x,c(y,z)) -> +#(x,y) -> +#(6(),8()) -> c#(1(),4()) c#(x,c(y,z)) -> +#(x,y) -> +#(6(),9()) -> c#(1(),5()) c#(x,c(y,z)) -> +#(x,y) -> +#(7(),3()) -> c#(1(),0()) c#(x,c(y,z)) -> +#(x,y) -> +#(7(),4()) -> c#(1(),1()) c#(x,c(y,z)) -> +#(x,y) -> +#(7(),5()) -> c#(1(),2()) c#(x,c(y,z)) -> +#(x,y) -> +#(7(),6()) -> c#(1(),3()) c#(x,c(y,z)) -> +#(x,y) -> +#(7(),7()) -> c#(1(),4()) c#(x,c(y,z)) -> +#(x,y) -> +#(7(),8()) -> c#(1(),5()) c#(x,c(y,z)) -> +#(x,y) -> +#(7(),9()) -> c#(1(),6()) c#(x,c(y,z)) -> +#(x,y) -> +#(8(),2()) -> c#(1(),0()) c#(x,c(y,z)) -> +#(x,y) -> +#(8(),3()) -> c#(1(),1()) c#(x,c(y,z)) -> +#(x,y) -> +#(8(),4()) -> c#(1(),2()) c#(x,c(y,z)) -> +#(x,y) -> +#(8(),5()) -> c#(1(),3()) c#(x,c(y,z)) -> +#(x,y) -> +#(8(),6()) -> c#(1(),4()) c#(x,c(y,z)) -> +#(x,y) -> +#(8(),7()) -> c#(1(),5()) c#(x,c(y,z)) -> +#(x,y) -> +#(8(),8()) -> c#(1(),6()) c#(x,c(y,z)) -> +#(x,y) -> +#(8(),9()) -> c#(1(),7()) c#(x,c(y,z)) -> +#(x,y) -> +#(9(),1()) -> c#(1(),0()) c#(x,c(y,z)) -> +#(x,y) -> +#(9(),2()) -> c#(1(),1()) c#(x,c(y,z)) -> +#(x,y) -> +#(9(),3()) -> c#(1(),2()) c#(x,c(y,z)) -> +#(x,y) -> +#(9(),4()) -> c#(1(),3()) c#(x,c(y,z)) -> +#(x,y) -> +#(9(),5()) -> c#(1(),4()) c#(x,c(y,z)) -> +#(x,y) -> +#(9(),6()) -> c#(1(),5()) c#(x,c(y,z)) -> +#(x,y) -> +#(9(),7()) -> c#(1(),6()) c#(x,c(y,z)) -> +#(x,y) -> +#(9(),8()) -> c#(1(),7()) c#(x,c(y,z)) -> +#(x,y) -> +#(9(),9()) -> c#(1(),8()) c#(x,c(y,z)) -> +#(x,y) -> +#(x,c(y,z)) -> +#(x,z) c#(x,c(y,z)) -> +#(x,y) -> +#(x,c(y,z)) -> c#(y,+(x,z)) c#(x,c(y,z)) -> +#(x,y) -> +#(c(x,y),z) -> +#(y,z) c#(x,c(y,z)) -> +#(x,y) -> +#(c(x,y),z) -> c#(x,+(y,z)) +#(c(x,y),z) -> c#(x,+(y,z)) -> c#(x,c(y,z)) -> +#(x,y) +#(c(x,y),z) -> c#(x,+(y,z)) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(c(x,y),z) -> +#(y,z) -> +#(1(),9()) -> c#(1(),0()) +#(c(x,y),z) -> +#(y,z) -> +#(2(),8()) -> c#(1(),0()) +#(c(x,y),z) -> +#(y,z) -> +#(2(),9()) -> c#(1(),1()) +#(c(x,y),z) -> +#(y,z) -> +#(3(),7()) -> c#(1(),0()) +#(c(x,y),z) -> +#(y,z) -> +#(3(),8()) -> c#(1(),1()) +#(c(x,y),z) -> +#(y,z) -> +#(3(),9()) -> c#(1(),2()) +#(c(x,y),z) -> +#(y,z) -> +#(4(),6()) -> c#(1(),0()) +#(c(x,y),z) -> +#(y,z) -> +#(4(),7()) -> c#(1(),1()) +#(c(x,y),z) -> +#(y,z) -> +#(4(),8()) -> c#(1(),2()) +#(c(x,y),z) -> +#(y,z) -> +#(4(),9()) -> c#(1(),3()) +#(c(x,y),z) -> +#(y,z) -> +#(5(),5()) -> c#(1(),0()) +#(c(x,y),z) -> +#(y,z) -> +#(5(),6()) -> c#(1(),1()) +#(c(x,y),z) -> +#(y,z) -> +#(5(),7()) -> c#(1(),2()) +#(c(x,y),z) -> +#(y,z) -> +#(5(),8()) -> c#(1(),3()) +#(c(x,y),z) -> +#(y,z) -> +#(5(),9()) -> c#(1(),4()) +#(c(x,y),z) -> +#(y,z) -> +#(6(),4()) -> c#(1(),0()) +#(c(x,y),z) -> +#(y,z) -> +#(6(),5()) -> c#(1(),1()) +#(c(x,y),z) -> +#(y,z) -> +#(6(),6()) -> c#(1(),2()) +#(c(x,y),z) -> +#(y,z) -> +#(6(),7()) -> c#(1(),3()) +#(c(x,y),z) -> +#(y,z) -> +#(6(),8()) -> c#(1(),4()) +#(c(x,y),z) -> +#(y,z) -> +#(6(),9()) -> c#(1(),5()) +#(c(x,y),z) -> +#(y,z) -> +#(7(),3()) -> c#(1(),0()) +#(c(x,y),z) -> +#(y,z) -> +#(7(),4()) -> c#(1(),1()) +#(c(x,y),z) -> +#(y,z) -> +#(7(),5()) -> c#(1(),2()) +#(c(x,y),z) -> +#(y,z) -> +#(7(),6()) -> c#(1(),3()) +#(c(x,y),z) -> +#(y,z) -> +#(7(),7()) -> c#(1(),4()) +#(c(x,y),z) -> +#(y,z) -> +#(7(),8()) -> c#(1(),5()) +#(c(x,y),z) -> +#(y,z) -> +#(7(),9()) -> c#(1(),6()) +#(c(x,y),z) -> +#(y,z) -> +#(8(),2()) -> c#(1(),0()) +#(c(x,y),z) -> +#(y,z) -> +#(8(),3()) -> c#(1(),1()) +#(c(x,y),z) -> +#(y,z) -> +#(8(),4()) -> c#(1(),2()) +#(c(x,y),z) -> +#(y,z) -> +#(8(),5()) -> c#(1(),3()) +#(c(x,y),z) -> +#(y,z) -> +#(8(),6()) -> c#(1(),4()) +#(c(x,y),z) -> +#(y,z) -> +#(8(),7()) -> c#(1(),5()) +#(c(x,y),z) -> +#(y,z) -> +#(8(),8()) -> c#(1(),6()) +#(c(x,y),z) -> +#(y,z) -> +#(8(),9()) -> c#(1(),7()) +#(c(x,y),z) -> +#(y,z) -> +#(9(),1()) -> c#(1(),0()) +#(c(x,y),z) -> +#(y,z) -> +#(9(),2()) -> c#(1(),1()) +#(c(x,y),z) -> +#(y,z) -> +#(9(),3()) -> c#(1(),2()) +#(c(x,y),z) -> +#(y,z) -> +#(9(),4()) -> c#(1(),3()) +#(c(x,y),z) -> +#(y,z) -> +#(9(),5()) -> c#(1(),4()) +#(c(x,y),z) -> +#(y,z) -> +#(9(),6()) -> c#(1(),5()) +#(c(x,y),z) -> +#(y,z) -> +#(9(),7()) -> c#(1(),6()) +#(c(x,y),z) -> +#(y,z) -> +#(9(),8()) -> c#(1(),7()) +#(c(x,y),z) -> +#(y,z) -> +#(9(),9()) -> c#(1(),8()) +#(c(x,y),z) -> +#(y,z) -> +#(x,c(y,z)) -> +#(x,z) +#(c(x,y),z) -> +#(y,z) -> +#(x,c(y,z)) -> c#(y,+(x,z)) +#(c(x,y),z) -> +#(y,z) -> +#(c(x,y),z) -> +#(y,z) +#(c(x,y),z) -> +#(y,z) -> +#(c(x,y),z) -> c#(x,+(y,z)) +#(x,c(y,z)) -> c#(y,+(x,z)) -> c#(x,c(y,z)) -> +#(x,y) +#(x,c(y,z)) -> c#(y,+(x,z)) -> c#(x,c(y,z)) -> c#(+(x,y),z) +#(x,c(y,z)) -> +#(x,z) -> +#(1(),9()) -> c#(1(),0()) +#(x,c(y,z)) -> +#(x,z) -> +#(2(),8()) -> c#(1(),0()) +#(x,c(y,z)) -> +#(x,z) -> +#(2(),9()) -> c#(1(),1()) +#(x,c(y,z)) -> +#(x,z) -> +#(3(),7()) -> c#(1(),0()) +#(x,c(y,z)) -> +#(x,z) -> +#(3(),8()) -> c#(1(),1()) +#(x,c(y,z)) -> +#(x,z) -> +#(3(),9()) -> c#(1(),2()) +#(x,c(y,z)) -> +#(x,z) -> +#(4(),6()) -> c#(1(),0()) +#(x,c(y,z)) -> +#(x,z) -> +#(4(),7()) -> c#(1(),1()) +#(x,c(y,z)) -> +#(x,z) -> +#(4(),8()) -> c#(1(),2()) +#(x,c(y,z)) -> +#(x,z) -> +#(4(),9()) -> c#(1(),3()) +#(x,c(y,z)) -> +#(x,z) -> +#(5(),5()) -> c#(1(),0()) +#(x,c(y,z)) -> +#(x,z) -> +#(5(),6()) -> c#(1(),1()) +#(x,c(y,z)) -> +#(x,z) -> +#(5(),7()) -> c#(1(),2()) +#(x,c(y,z)) -> +#(x,z) -> +#(5(),8()) -> c#(1(),3()) +#(x,c(y,z)) -> +#(x,z) -> +#(5(),9()) -> c#(1(),4()) +#(x,c(y,z)) -> +#(x,z) -> +#(6(),4()) -> c#(1(),0()) +#(x,c(y,z)) -> +#(x,z) -> +#(6(),5()) -> c#(1(),1()) +#(x,c(y,z)) -> +#(x,z) -> +#(6(),6()) -> c#(1(),2()) +#(x,c(y,z)) -> +#(x,z) -> +#(6(),7()) -> c#(1(),3()) +#(x,c(y,z)) -> +#(x,z) -> +#(6(),8()) -> c#(1(),4()) +#(x,c(y,z)) -> +#(x,z) -> +#(6(),9()) -> c#(1(),5()) +#(x,c(y,z)) -> +#(x,z) -> +#(7(),3()) -> c#(1(),0()) +#(x,c(y,z)) -> +#(x,z) -> +#(7(),4()) -> c#(1(),1()) +#(x,c(y,z)) -> +#(x,z) -> +#(7(),5()) -> c#(1(),2()) +#(x,c(y,z)) -> +#(x,z) -> +#(7(),6()) -> c#(1(),3()) +#(x,c(y,z)) -> +#(x,z) -> +#(7(),7()) -> c#(1(),4()) +#(x,c(y,z)) -> +#(x,z) -> +#(7(),8()) -> c#(1(),5()) +#(x,c(y,z)) -> +#(x,z) -> +#(7(),9()) -> c#(1(),6()) +#(x,c(y,z)) -> +#(x,z) -> +#(8(),2()) -> c#(1(),0()) +#(x,c(y,z)) -> +#(x,z) -> +#(8(),3()) -> c#(1(),1()) +#(x,c(y,z)) -> +#(x,z) -> +#(8(),4()) -> c#(1(),2()) +#(x,c(y,z)) -> +#(x,z) -> +#(8(),5()) -> c#(1(),3()) +#(x,c(y,z)) -> +#(x,z) -> +#(8(),6()) -> c#(1(),4()) +#(x,c(y,z)) -> +#(x,z) -> +#(8(),7()) -> c#(1(),5()) +#(x,c(y,z)) -> +#(x,z) -> +#(8(),8()) -> c#(1(),6()) +#(x,c(y,z)) -> +#(x,z) -> +#(8(),9()) -> c#(1(),7()) +#(x,c(y,z)) -> +#(x,z) -> +#(9(),1()) -> c#(1(),0()) +#(x,c(y,z)) -> +#(x,z) -> +#(9(),2()) -> c#(1(),1()) +#(x,c(y,z)) -> +#(x,z) -> +#(9(),3()) -> c#(1(),2()) +#(x,c(y,z)) -> +#(x,z) -> +#(9(),4()) -> c#(1(),3()) +#(x,c(y,z)) -> +#(x,z) -> +#(9(),5()) -> c#(1(),4()) +#(x,c(y,z)) -> +#(x,z) -> +#(9(),6()) -> c#(1(),5()) +#(x,c(y,z)) -> +#(x,z) -> +#(9(),7()) -> c#(1(),6()) +#(x,c(y,z)) -> +#(x,z) -> +#(9(),8()) -> c#(1(),7()) +#(x,c(y,z)) -> +#(x,z) -> +#(9(),9()) -> c#(1(),8()) +#(x,c(y,z)) -> +#(x,z) -> +#(x,c(y,z)) -> +#(x,z) +#(x,c(y,z)) -> +#(x,z) -> +#(x,c(y,z)) -> c#(y,+(x,z)) +#(x,c(y,z)) -> +#(x,z) -> +#(c(x,y),z) -> +#(y,z) +#(x,c(y,z)) -> +#(x,z) -> +#(c(x,y),z) -> c#(x,+(y,z)) SCC Processor: #sccs: 1 #rules: 6 #arcs: 153/2601 DPs: c#(x,c(y,z)) -> c#(+(x,y),z) c#(x,c(y,z)) -> +#(x,y) +#(c(x,y),z) -> c#(x,+(y,z)) +#(c(x,y),z) -> +#(y,z) +#(x,c(y,z)) -> c#(y,+(x,z)) +#(x,c(y,z)) -> +#(x,z) TRS: +(0(),0()) -> 0() +(0(),1()) -> 1() +(0(),2()) -> 2() +(0(),3()) -> 3() +(0(),4()) -> 4() +(0(),5()) -> 5() +(0(),6()) -> 6() +(0(),7()) -> 7() +(0(),8()) -> 8() +(0(),9()) -> 9() +(1(),0()) -> 1() +(1(),1()) -> 2() +(1(),2()) -> 3() +(1(),3()) -> 4() +(1(),4()) -> 5() +(1(),5()) -> 6() +(1(),6()) -> 7() +(1(),7()) -> 8() +(1(),8()) -> 9() +(1(),9()) -> c(1(),0()) +(2(),0()) -> 2() +(2(),1()) -> 3() +(2(),2()) -> 4() +(2(),3()) -> 5() +(2(),4()) -> 6() +(2(),5()) -> 7() +(2(),6()) -> 8() +(2(),7()) -> 9() +(2(),8()) -> c(1(),0()) +(2(),9()) -> c(1(),1()) +(3(),0()) -> 3() +(3(),1()) -> 4() +(3(),2()) -> 5() +(3(),3()) -> 6() +(3(),4()) -> 7() +(3(),5()) -> 8() +(3(),6()) -> 9() +(3(),7()) -> c(1(),0()) +(3(),8()) -> c(1(),1()) +(3(),9()) -> c(1(),2()) +(4(),0()) -> 4() +(4(),1()) -> 5() +(4(),2()) -> 6() +(4(),3()) -> 7() +(4(),4()) -> 8() +(4(),5()) -> 9() +(4(),6()) -> c(1(),0()) +(4(),7()) -> c(1(),1()) +(4(),8()) -> c(1(),2()) +(4(),9()) -> c(1(),3()) +(5(),0()) -> 5() +(5(),1()) -> 6() +(5(),2()) -> 7() +(5(),3()) -> 8() +(5(),4()) -> 9() +(5(),5()) -> c(1(),0()) +(5(),6()) -> c(1(),1()) +(5(),7()) -> c(1(),2()) +(5(),8()) -> c(1(),3()) +(5(),9()) -> c(1(),4()) +(6(),0()) -> 6() +(6(),1()) -> 7() +(6(),2()) -> 8() +(6(),3()) -> 9() +(6(),4()) -> c(1(),0()) +(6(),5()) -> c(1(),1()) +(6(),6()) -> c(1(),2()) +(6(),7()) -> c(1(),3()) +(6(),8()) -> c(1(),4()) +(6(),9()) -> c(1(),5()) +(7(),0()) -> 7() +(7(),1()) -> 8() +(7(),2()) -> 9() +(7(),3()) -> c(1(),0()) +(7(),4()) -> c(1(),1()) +(7(),5()) -> c(1(),2()) +(7(),6()) -> c(1(),3()) +(7(),7()) -> c(1(),4()) +(7(),8()) -> c(1(),5()) +(7(),9()) -> c(1(),6()) +(8(),0()) -> 8() +(8(),1()) -> 9() +(8(),2()) -> c(1(),0()) +(8(),3()) -> c(1(),1()) +(8(),4()) -> c(1(),2()) +(8(),5()) -> c(1(),3()) +(8(),6()) -> c(1(),4()) +(8(),7()) -> c(1(),5()) +(8(),8()) -> c(1(),6()) +(8(),9()) -> c(1(),7()) +(9(),0()) -> 9() +(9(),1()) -> c(1(),0()) +(9(),2()) -> c(1(),1()) +(9(),3()) -> c(1(),2()) +(9(),4()) -> c(1(),3()) +(9(),5()) -> c(1(),4()) +(9(),6()) -> c(1(),5()) +(9(),7()) -> c(1(),6()) +(9(),8()) -> c(1(),7()) +(9(),9()) -> c(1(),8()) +(x,c(y,z)) -> c(y,+(x,z)) +(c(x,y),z) -> c(x,+(y,z)) c(0(),x) -> x c(x,c(y,z)) -> c(+(x,y),z) Matrix Interpretation Processor: dim=1 interpretation: [c#](x0, x1) = 4x0 + 4x1, [+#](x0, x1) = 4x0 + 4x1, [c](x0, x1) = x0 + x1 + 4, [9] = 2, [8] = 2, [7] = 3, [6] = 4, [5] = 4, [4] = 5, [3] = 4, [2] = 4, [1] = 0, [+](x0, x1) = x0 + x1 + 4, [0] = 1 orientation: c#(x,c(y,z)) = 4x + 4y + 4z + 16 >= 4x + 4y + 4z + 16 = c#(+(x,y),z) c#(x,c(y,z)) = 4x + 4y + 4z + 16 >= 4x + 4y = +#(x,y) +#(c(x,y),z) = 4x + 4y + 4z + 16 >= 4x + 4y + 4z + 16 = c#(x,+(y,z)) +#(c(x,y),z) = 4x + 4y + 4z + 16 >= 4y + 4z = +#(y,z) +#(x,c(y,z)) = 4x + 4y + 4z + 16 >= 4x + 4y + 4z + 16 = c#(y,+(x,z)) +#(x,c(y,z)) = 4x + 4y + 4z + 16 >= 4x + 4z = +#(x,z) +(0(),0()) = 6 >= 1 = 0() +(0(),1()) = 5 >= 0 = 1() +(0(),2()) = 9 >= 4 = 2() +(0(),3()) = 9 >= 4 = 3() +(0(),4()) = 10 >= 5 = 4() +(0(),5()) = 9 >= 4 = 5() +(0(),6()) = 9 >= 4 = 6() +(0(),7()) = 8 >= 3 = 7() +(0(),8()) = 7 >= 2 = 8() +(0(),9()) = 7 >= 2 = 9() +(1(),0()) = 5 >= 0 = 1() +(1(),1()) = 4 >= 4 = 2() +(1(),2()) = 8 >= 4 = 3() +(1(),3()) = 8 >= 5 = 4() +(1(),4()) = 9 >= 4 = 5() +(1(),5()) = 8 >= 4 = 6() +(1(),6()) = 8 >= 3 = 7() +(1(),7()) = 7 >= 2 = 8() +(1(),8()) = 6 >= 2 = 9() +(1(),9()) = 6 >= 5 = c(1(),0()) +(2(),0()) = 9 >= 4 = 2() +(2(),1()) = 8 >= 4 = 3() +(2(),2()) = 12 >= 5 = 4() +(2(),3()) = 12 >= 4 = 5() +(2(),4()) = 13 >= 4 = 6() +(2(),5()) = 12 >= 3 = 7() +(2(),6()) = 12 >= 2 = 8() +(2(),7()) = 11 >= 2 = 9() +(2(),8()) = 10 >= 5 = c(1(),0()) +(2(),9()) = 10 >= 4 = c(1(),1()) +(3(),0()) = 9 >= 4 = 3() +(3(),1()) = 8 >= 5 = 4() +(3(),2()) = 12 >= 4 = 5() +(3(),3()) = 12 >= 4 = 6() +(3(),4()) = 13 >= 3 = 7() +(3(),5()) = 12 >= 2 = 8() +(3(),6()) = 12 >= 2 = 9() +(3(),7()) = 11 >= 5 = c(1(),0()) +(3(),8()) = 10 >= 4 = c(1(),1()) +(3(),9()) = 10 >= 8 = c(1(),2()) +(4(),0()) = 10 >= 5 = 4() +(4(),1()) = 9 >= 4 = 5() +(4(),2()) = 13 >= 4 = 6() +(4(),3()) = 13 >= 3 = 7() +(4(),4()) = 14 >= 2 = 8() +(4(),5()) = 13 >= 2 = 9() +(4(),6()) = 13 >= 5 = c(1(),0()) +(4(),7()) = 12 >= 4 = c(1(),1()) +(4(),8()) = 11 >= 8 = c(1(),2()) +(4(),9()) = 11 >= 8 = c(1(),3()) +(5(),0()) = 9 >= 4 = 5() +(5(),1()) = 8 >= 4 = 6() +(5(),2()) = 12 >= 3 = 7() +(5(),3()) = 12 >= 2 = 8() +(5(),4()) = 13 >= 2 = 9() +(5(),5()) = 12 >= 5 = c(1(),0()) +(5(),6()) = 12 >= 4 = c(1(),1()) +(5(),7()) = 11 >= 8 = c(1(),2()) +(5(),8()) = 10 >= 8 = c(1(),3()) +(5(),9()) = 10 >= 9 = c(1(),4()) +(6(),0()) = 9 >= 4 = 6() +(6(),1()) = 8 >= 3 = 7() +(6(),2()) = 12 >= 2 = 8() +(6(),3()) = 12 >= 2 = 9() +(6(),4()) = 13 >= 5 = c(1(),0()) +(6(),5()) = 12 >= 4 = c(1(),1()) +(6(),6()) = 12 >= 8 = c(1(),2()) +(6(),7()) = 11 >= 8 = c(1(),3()) +(6(),8()) = 10 >= 9 = c(1(),4()) +(6(),9()) = 10 >= 8 = c(1(),5()) +(7(),0()) = 8 >= 3 = 7() +(7(),1()) = 7 >= 2 = 8() +(7(),2()) = 11 >= 2 = 9() +(7(),3()) = 11 >= 5 = c(1(),0()) +(7(),4()) = 12 >= 4 = c(1(),1()) +(7(),5()) = 11 >= 8 = c(1(),2()) +(7(),6()) = 11 >= 8 = c(1(),3()) +(7(),7()) = 10 >= 9 = c(1(),4()) +(7(),8()) = 9 >= 8 = c(1(),5()) +(7(),9()) = 9 >= 8 = c(1(),6()) +(8(),0()) = 7 >= 2 = 8() +(8(),1()) = 6 >= 2 = 9() +(8(),2()) = 10 >= 5 = c(1(),0()) +(8(),3()) = 10 >= 4 = c(1(),1()) +(8(),4()) = 11 >= 8 = c(1(),2()) +(8(),5()) = 10 >= 8 = c(1(),3()) +(8(),6()) = 10 >= 9 = c(1(),4()) +(8(),7()) = 9 >= 8 = c(1(),5()) +(8(),8()) = 8 >= 8 = c(1(),6()) +(8(),9()) = 8 >= 7 = c(1(),7()) +(9(),0()) = 7 >= 2 = 9() +(9(),1()) = 6 >= 5 = c(1(),0()) +(9(),2()) = 10 >= 4 = c(1(),1()) +(9(),3()) = 10 >= 8 = c(1(),2()) +(9(),4()) = 11 >= 8 = c(1(),3()) +(9(),5()) = 10 >= 9 = c(1(),4()) +(9(),6()) = 10 >= 8 = c(1(),5()) +(9(),7()) = 9 >= 8 = c(1(),6()) +(9(),8()) = 8 >= 7 = c(1(),7()) +(9(),9()) = 8 >= 6 = c(1(),8()) +(x,c(y,z)) = x + y + z + 8 >= x + y + z + 8 = c(y,+(x,z)) +(c(x,y),z) = x + y + z + 8 >= x + y + z + 8 = c(x,+(y,z)) c(0(),x) = x + 5 >= x = x c(x,c(y,z)) = x + y + z + 8 >= x + y + z + 8 = c(+(x,y),z) problem: DPs: c#(x,c(y,z)) -> c#(+(x,y),z) +#(c(x,y),z) -> c#(x,+(y,z)) +#(x,c(y,z)) -> c#(y,+(x,z)) TRS: +(0(),0()) -> 0() +(0(),1()) -> 1() +(0(),2()) -> 2() +(0(),3()) -> 3() +(0(),4()) -> 4() +(0(),5()) -> 5() +(0(),6()) -> 6() +(0(),7()) -> 7() +(0(),8()) -> 8() +(0(),9()) -> 9() +(1(),0()) -> 1() +(1(),1()) -> 2() +(1(),2()) -> 3() +(1(),3()) -> 4() +(1(),4()) -> 5() +(1(),5()) -> 6() +(1(),6()) -> 7() +(1(),7()) -> 8() +(1(),8()) -> 9() +(1(),9()) -> c(1(),0()) +(2(),0()) -> 2() +(2(),1()) -> 3() +(2(),2()) -> 4() +(2(),3()) -> 5() +(2(),4()) -> 6() +(2(),5()) -> 7() +(2(),6()) -> 8() +(2(),7()) -> 9() +(2(),8()) -> c(1(),0()) +(2(),9()) -> c(1(),1()) +(3(),0()) -> 3() +(3(),1()) -> 4() +(3(),2()) -> 5() +(3(),3()) -> 6() +(3(),4()) -> 7() +(3(),5()) -> 8() +(3(),6()) -> 9() +(3(),7()) -> c(1(),0()) +(3(),8()) -> c(1(),1()) +(3(),9()) -> c(1(),2()) +(4(),0()) -> 4() +(4(),1()) -> 5() +(4(),2()) -> 6() +(4(),3()) -> 7() +(4(),4()) -> 8() +(4(),5()) -> 9() +(4(),6()) -> c(1(),0()) +(4(),7()) -> c(1(),1()) +(4(),8()) -> c(1(),2()) +(4(),9()) -> c(1(),3()) +(5(),0()) -> 5() +(5(),1()) -> 6() +(5(),2()) -> 7() +(5(),3()) -> 8() +(5(),4()) -> 9() +(5(),5()) -> c(1(),0()) +(5(),6()) -> c(1(),1()) +(5(),7()) -> c(1(),2()) +(5(),8()) -> c(1(),3()) +(5(),9()) -> c(1(),4()) +(6(),0()) -> 6() +(6(),1()) -> 7() +(6(),2()) -> 8() +(6(),3()) -> 9() +(6(),4()) -> c(1(),0()) +(6(),5()) -> c(1(),1()) +(6(),6()) -> c(1(),2()) +(6(),7()) -> c(1(),3()) +(6(),8()) -> c(1(),4()) +(6(),9()) -> c(1(),5()) +(7(),0()) -> 7() +(7(),1()) -> 8() +(7(),2()) -> 9() +(7(),3()) -> c(1(),0()) +(7(),4()) -> c(1(),1()) +(7(),5()) -> c(1(),2()) +(7(),6()) -> c(1(),3()) +(7(),7()) -> c(1(),4()) +(7(),8()) -> c(1(),5()) +(7(),9()) -> c(1(),6()) +(8(),0()) -> 8() +(8(),1()) -> 9() +(8(),2()) -> c(1(),0()) +(8(),3()) -> c(1(),1()) +(8(),4()) -> c(1(),2()) +(8(),5()) -> c(1(),3()) +(8(),6()) -> c(1(),4()) +(8(),7()) -> c(1(),5()) +(8(),8()) -> c(1(),6()) +(8(),9()) -> c(1(),7()) +(9(),0()) -> 9() +(9(),1()) -> c(1(),0()) +(9(),2()) -> c(1(),1()) +(9(),3()) -> c(1(),2()) +(9(),4()) -> c(1(),3()) +(9(),5()) -> c(1(),4()) +(9(),6()) -> c(1(),5()) +(9(),7()) -> c(1(),6()) +(9(),8()) -> c(1(),7()) +(9(),9()) -> c(1(),8()) +(x,c(y,z)) -> c(y,+(x,z)) +(c(x,y),z) -> c(x,+(y,z)) c(0(),x) -> x c(x,c(y,z)) -> c(+(x,y),z) SCC Processor: #sccs: 1 #rules: 1 #arcs: 18/9 DPs: c#(x,c(y,z)) -> c#(+(x,y),z) TRS: +(0(),0()) -> 0() +(0(),1()) -> 1() +(0(),2()) -> 2() +(0(),3()) -> 3() +(0(),4()) -> 4() +(0(),5()) -> 5() +(0(),6()) -> 6() +(0(),7()) -> 7() +(0(),8()) -> 8() +(0(),9()) -> 9() +(1(),0()) -> 1() +(1(),1()) -> 2() +(1(),2()) -> 3() +(1(),3()) -> 4() +(1(),4()) -> 5() +(1(),5()) -> 6() +(1(),6()) -> 7() +(1(),7()) -> 8() +(1(),8()) -> 9() +(1(),9()) -> c(1(),0()) +(2(),0()) -> 2() +(2(),1()) -> 3() +(2(),2()) -> 4() +(2(),3()) -> 5() +(2(),4()) -> 6() +(2(),5()) -> 7() +(2(),6()) -> 8() +(2(),7()) -> 9() +(2(),8()) -> c(1(),0()) +(2(),9()) -> c(1(),1()) +(3(),0()) -> 3() +(3(),1()) -> 4() +(3(),2()) -> 5() +(3(),3()) -> 6() +(3(),4()) -> 7() +(3(),5()) -> 8() +(3(),6()) -> 9() +(3(),7()) -> c(1(),0()) +(3(),8()) -> c(1(),1()) +(3(),9()) -> c(1(),2()) +(4(),0()) -> 4() +(4(),1()) -> 5() +(4(),2()) -> 6() +(4(),3()) -> 7() +(4(),4()) -> 8() +(4(),5()) -> 9() +(4(),6()) -> c(1(),0()) +(4(),7()) -> c(1(),1()) +(4(),8()) -> c(1(),2()) +(4(),9()) -> c(1(),3()) +(5(),0()) -> 5() +(5(),1()) -> 6() +(5(),2()) -> 7() +(5(),3()) -> 8() +(5(),4()) -> 9() +(5(),5()) -> c(1(),0()) +(5(),6()) -> c(1(),1()) +(5(),7()) -> c(1(),2()) +(5(),8()) -> c(1(),3()) +(5(),9()) -> c(1(),4()) +(6(),0()) -> 6() +(6(),1()) -> 7() +(6(),2()) -> 8() +(6(),3()) -> 9() +(6(),4()) -> c(1(),0()) +(6(),5()) -> c(1(),1()) +(6(),6()) -> c(1(),2()) +(6(),7()) -> c(1(),3()) +(6(),8()) -> c(1(),4()) +(6(),9()) -> c(1(),5()) +(7(),0()) -> 7() +(7(),1()) -> 8() +(7(),2()) -> 9() +(7(),3()) -> c(1(),0()) +(7(),4()) -> c(1(),1()) +(7(),5()) -> c(1(),2()) +(7(),6()) -> c(1(),3()) +(7(),7()) -> c(1(),4()) +(7(),8()) -> c(1(),5()) +(7(),9()) -> c(1(),6()) +(8(),0()) -> 8() +(8(),1()) -> 9() +(8(),2()) -> c(1(),0()) +(8(),3()) -> c(1(),1()) +(8(),4()) -> c(1(),2()) +(8(),5()) -> c(1(),3()) +(8(),6()) -> c(1(),4()) +(8(),7()) -> c(1(),5()) +(8(),8()) -> c(1(),6()) +(8(),9()) -> c(1(),7()) +(9(),0()) -> 9() +(9(),1()) -> c(1(),0()) +(9(),2()) -> c(1(),1()) +(9(),3()) -> c(1(),2()) +(9(),4()) -> c(1(),3()) +(9(),5()) -> c(1(),4()) +(9(),6()) -> c(1(),5()) +(9(),7()) -> c(1(),6()) +(9(),8()) -> c(1(),7()) +(9(),9()) -> c(1(),8()) +(x,c(y,z)) -> c(y,+(x,z)) +(c(x,y),z) -> c(x,+(y,z)) c(0(),x) -> x c(x,c(y,z)) -> c(+(x,y),z) Subterm Criterion Processor: simple projection: pi(c#) = 1 problem: DPs: TRS: +(0(),0()) -> 0() +(0(),1()) -> 1() +(0(),2()) -> 2() +(0(),3()) -> 3() +(0(),4()) -> 4() +(0(),5()) -> 5() +(0(),6()) -> 6() +(0(),7()) -> 7() +(0(),8()) -> 8() +(0(),9()) -> 9() +(1(),0()) -> 1() +(1(),1()) -> 2() +(1(),2()) -> 3() +(1(),3()) -> 4() +(1(),4()) -> 5() +(1(),5()) -> 6() +(1(),6()) -> 7() +(1(),7()) -> 8() +(1(),8()) -> 9() +(1(),9()) -> c(1(),0()) +(2(),0()) -> 2() +(2(),1()) -> 3() +(2(),2()) -> 4() +(2(),3()) -> 5() +(2(),4()) -> 6() +(2(),5()) -> 7() +(2(),6()) -> 8() +(2(),7()) -> 9() +(2(),8()) -> c(1(),0()) +(2(),9()) -> c(1(),1()) +(3(),0()) -> 3() +(3(),1()) -> 4() +(3(),2()) -> 5() +(3(),3()) -> 6() +(3(),4()) -> 7() +(3(),5()) -> 8() +(3(),6()) -> 9() +(3(),7()) -> c(1(),0()) +(3(),8()) -> c(1(),1()) +(3(),9()) -> c(1(),2()) +(4(),0()) -> 4() +(4(),1()) -> 5() +(4(),2()) -> 6() +(4(),3()) -> 7() +(4(),4()) -> 8() +(4(),5()) -> 9() +(4(),6()) -> c(1(),0()) +(4(),7()) -> c(1(),1()) +(4(),8()) -> c(1(),2()) +(4(),9()) -> c(1(),3()) +(5(),0()) -> 5() +(5(),1()) -> 6() +(5(),2()) -> 7() +(5(),3()) -> 8() +(5(),4()) -> 9() +(5(),5()) -> c(1(),0()) +(5(),6()) -> c(1(),1()) +(5(),7()) -> c(1(),2()) +(5(),8()) -> c(1(),3()) +(5(),9()) -> c(1(),4()) +(6(),0()) -> 6() +(6(),1()) -> 7() +(6(),2()) -> 8() +(6(),3()) -> 9() +(6(),4()) -> c(1(),0()) +(6(),5()) -> c(1(),1()) +(6(),6()) -> c(1(),2()) +(6(),7()) -> c(1(),3()) +(6(),8()) -> c(1(),4()) +(6(),9()) -> c(1(),5()) +(7(),0()) -> 7() +(7(),1()) -> 8() +(7(),2()) -> 9() +(7(),3()) -> c(1(),0()) +(7(),4()) -> c(1(),1()) +(7(),5()) -> c(1(),2()) +(7(),6()) -> c(1(),3()) +(7(),7()) -> c(1(),4()) +(7(),8()) -> c(1(),5()) +(7(),9()) -> c(1(),6()) +(8(),0()) -> 8() +(8(),1()) -> 9() +(8(),2()) -> c(1(),0()) +(8(),3()) -> c(1(),1()) +(8(),4()) -> c(1(),2()) +(8(),5()) -> c(1(),3()) +(8(),6()) -> c(1(),4()) +(8(),7()) -> c(1(),5()) +(8(),8()) -> c(1(),6()) +(8(),9()) -> c(1(),7()) +(9(),0()) -> 9() +(9(),1()) -> c(1(),0()) +(9(),2()) -> c(1(),1()) +(9(),3()) -> c(1(),2()) +(9(),4()) -> c(1(),3()) +(9(),5()) -> c(1(),4()) +(9(),6()) -> c(1(),5()) +(9(),7()) -> c(1(),6()) +(9(),8()) -> c(1(),7()) +(9(),9()) -> c(1(),8()) +(x,c(y,z)) -> c(y,+(x,z)) +(c(x,y),z) -> c(x,+(y,z)) c(0(),x) -> x c(x,c(y,z)) -> c(+(x,y),z) Qed