Tool CaT
stdout:
MAYBE
Problem:
0(#()) -> #()
+(#(),x) -> x
+(x,#()) -> x
+(0(x),0(y)) -> 0(+(x,y))
+(0(x),1(y)) -> 1(+(x,y))
+(1(x),0(y)) -> 1(+(x,y))
+(0(x),j(y)) -> j(+(x,y))
+(j(x),0(y)) -> j(+(x,y))
+(1(x),1(y)) -> j(+(+(x,y),1(#())))
+(j(x),j(y)) -> 1(+(+(x,y),j(#())))
+(1(x),j(y)) -> 0(+(x,y))
+(j(x),1(y)) -> 0(+(x,y))
+(+(x,y),z) -> +(x,+(y,z))
opp(#()) -> #()
opp(0(x)) -> 0(opp(x))
opp(1(x)) -> j(opp(x))
opp(j(x)) -> 1(opp(x))
-(x,y) -> +(x,opp(y))
*(#(),x) -> #()
*(0(x),y) -> 0(*(x,y))
*(1(x),y) -> +(0(*(x,y)),y)
*(j(x),y) -> -(0(*(x,y)),y)
*(*(x,y),z) -> *(x,*(y,z))
*(+(x,y),z) -> +(*(x,z),*(y,z))
*(x,+(y,z)) -> +(*(x,y),*(x,z))
Proof:
OpenTool IRC1
stdout:
MAYBE
Tool IRC2
stdout:
TIMEOUT
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: TIMEOUT
Input Problem: innermost runtime-complexity with respect to
Rules:
{ 0(#()) -> #()
, +(#(), x) -> x
, +(x, #()) -> x
, +(0(x), 0(y)) -> 0(+(x, y))
, +(0(x), 1(y)) -> 1(+(x, y))
, +(1(x), 0(y)) -> 1(+(x, y))
, +(0(x), j(y)) -> j(+(x, y))
, +(j(x), 0(y)) -> j(+(x, y))
, +(1(x), 1(y)) -> j(+(+(x, y), 1(#())))
, +(j(x), j(y)) -> 1(+(+(x, y), j(#())))
, +(1(x), j(y)) -> 0(+(x, y))
, +(j(x), 1(y)) -> 0(+(x, y))
, +(+(x, y), z) -> +(x, +(y, z))
, opp(#()) -> #()
, opp(0(x)) -> 0(opp(x))
, opp(1(x)) -> j(opp(x))
, opp(j(x)) -> 1(opp(x))
, -(x, y) -> +(x, opp(y))
, *(#(), x) -> #()
, *(0(x), y) -> 0(*(x, y))
, *(1(x), y) -> +(0(*(x, y)), y)
, *(j(x), y) -> -(0(*(x, y)), y)
, *(*(x, y), z) -> *(x, *(y, z))
, *(+(x, y), z) -> +(*(x, z), *(y, z))
, *(x, +(y, z)) -> +(*(x, y), *(x, z))}
Proof Output:
Computation stopped due to timeout after 60.0 secondsTool RC1
stdout:
MAYBE
Tool RC2
stdout:
TIMEOUT
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: TIMEOUT
Input Problem: runtime-complexity with respect to
Rules:
{ 0(#()) -> #()
, +(#(), x) -> x
, +(x, #()) -> x
, +(0(x), 0(y)) -> 0(+(x, y))
, +(0(x), 1(y)) -> 1(+(x, y))
, +(1(x), 0(y)) -> 1(+(x, y))
, +(0(x), j(y)) -> j(+(x, y))
, +(j(x), 0(y)) -> j(+(x, y))
, +(1(x), 1(y)) -> j(+(+(x, y), 1(#())))
, +(j(x), j(y)) -> 1(+(+(x, y), j(#())))
, +(1(x), j(y)) -> 0(+(x, y))
, +(j(x), 1(y)) -> 0(+(x, y))
, +(+(x, y), z) -> +(x, +(y, z))
, opp(#()) -> #()
, opp(0(x)) -> 0(opp(x))
, opp(1(x)) -> j(opp(x))
, opp(j(x)) -> 1(opp(x))
, -(x, y) -> +(x, opp(y))
, *(#(), x) -> #()
, *(0(x), y) -> 0(*(x, y))
, *(1(x), y) -> +(0(*(x, y)), y)
, *(j(x), y) -> -(0(*(x, y)), y)
, *(*(x, y), z) -> *(x, *(y, z))
, *(+(x, y), z) -> +(*(x, z), *(y, z))
, *(x, +(y, z)) -> +(*(x, y), *(x, z))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds