Problem: +(0(),y) -> y +(s(x),0()) -> s(x) +(s(x),s(y)) -> s(+(s(x),+(y,0()))) Proof: Complexity Transformation Processor: strict: +(0(),y) -> y +(s(x),0()) -> s(x) +(s(x),s(y)) -> s(+(s(x),+(y,0()))) weak: Matrix Interpretation Processor: dimension: 1 max_matrix: 1 interpretation: [s](x0) = x0, [+](x0, x1) = x0 + x1, [0] = 2 orientation: +(0(),y) = y + 2 >= y = y +(s(x),0()) = x + 2 >= x = s(x) +(s(x),s(y)) = x + y >= x + y + 2 = s(+(s(x),+(y,0()))) problem: strict: +(s(x),s(y)) -> s(+(s(x),+(y,0()))) weak: +(0(),y) -> y +(s(x),0()) -> s(x) Bounds Processor: bound: 2 enrichment: match automaton: final states: {3} transitions: s1(7) -> 3* s1(2) -> 17,7,5,6 s1(1) -> 17,7,5,6 +1(1,4) -> 5* +1(6,5) -> 7* +1(2,4) -> 5* 01() -> 4* s2(2) -> 19,18 s2(19) -> 19,7 s2(1) -> 19,18 +0(1,2) -> 3* +0(2,1) -> 3* +0(1,1) -> 3* +0(2,2) -> 3* +2(2,16) -> 17* +2(18,17) -> 19* +2(1,16) -> 17* s0(2) -> 1* s0(1) -> 1* 02() -> 16* 00() -> 2* 1 -> 3* 2 -> 3* 4 -> 5* 16 -> 17* problem: strict: weak: +(s(x),s(y)) -> s(+(s(x),+(y,0()))) +(0(),y) -> y +(s(x),0()) -> s(x) Qed