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