YES (ignored inputs)COMMENT from the collection of \cite{AT2012} Rewrite Rules: [ +(+(?x,?y),?z) -> +(?x,+(?y,?z)), +(?x,+(?y,?z)) -> +(+(?x,?y),?z), +(?x,?y) -> +(?y,?x) ] Apply Direct Methods... Inner CPs: [ +(+(+(?x_1,?y_1),?z_1),?z) = +(?x_1,+(+(?y_1,?z_1),?z)), +(+(?y_2,?x_2),?z) = +(?x_2,+(?y_2,?z)), +(?x_1,+(?x,+(?y,?z))) = +(+(?x_1,+(?x,?y)),?z), +(?x_1,+(?y_2,?x_2)) = +(+(?x_1,?x_2),?y_2), +(+(?x,+(?y,?z)),?z_1) = +(+(?x,?y),+(?z,?z_1)), +(?x_1,+(+(?x,?y),?z)) = +(+(?x_1,?x),+(?y,?z)) ] Outer CPs: [ +(?x,+(?y,+(?y_1,?z_1))) = +(+(+(?x,?y),?y_1),?z_1), +(?x,+(?y,?z)) = +(?z,+(?x,?y)), +(+(?x_1,?y_1),?z_1) = +(+(?y_1,?z_1),?x_1) ] not Overlay, check Termination... unknown/not Terminating unknown Knuth & Bendix Linear unknown Development Closed Strongly Closed Direct Methods: CR Final result: CR 178.trs: Success(CR) (1 msec.)