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))
+(1(x),1(y)) -> 0(+(+(x,y),1(#())))
+(+(x,y),z) -> +(x,+(y,z))
-(#(),x) -> #()
-(x,#()) -> x
-(0(x),0(y)) -> 0(-(x,y))
-(0(x),1(y)) -> 1(-(-(x,y),1(#())))
-(1(x),0(y)) -> 1(-(x,y))
-(1(x),1(y)) -> 0(-(x,y))
not(true()) -> false()
not(false()) -> true()
if(true(),x,y) -> x
if(false(),x,y) -> y
ge(0(x),0(y)) -> ge(x,y)
ge(0(x),1(y)) -> not(ge(y,x))
ge(1(x),0(y)) -> ge(x,y)
ge(1(x),1(y)) -> ge(x,y)
ge(x,#()) -> true()
ge(#(),0(x)) -> ge(#(),x)
ge(#(),1(x)) -> false()
log(x) -> -(log'(x),1(#()))
log'(#()) -> #()
log'(1(x)) -> +(log'(x),1(#()))
log'(0(x)) -> if(ge(x,1(#())),+(log'(x),1(#())),#())
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))
, +(1(x), 1(y)) -> 0(+(+(x, y), 1(#())))
, +(+(x, y), z) -> +(x, +(y, z))
, -(#(), x) -> #()
, -(x, #()) -> x
, -(0(x), 0(y)) -> 0(-(x, y))
, -(0(x), 1(y)) -> 1(-(-(x, y), 1(#())))
, -(1(x), 0(y)) -> 1(-(x, y))
, -(1(x), 1(y)) -> 0(-(x, y))
, not(true()) -> false()
, not(false()) -> true()
, if(true(), x, y) -> x
, if(false(), x, y) -> y
, ge(0(x), 0(y)) -> ge(x, y)
, ge(0(x), 1(y)) -> not(ge(y, x))
, ge(1(x), 0(y)) -> ge(x, y)
, ge(1(x), 1(y)) -> ge(x, y)
, ge(x, #()) -> true()
, ge(#(), 0(x)) -> ge(#(), x)
, ge(#(), 1(x)) -> false()
, log(x) -> -(log'(x), 1(#()))
, log'(#()) -> #()
, log'(1(x)) -> +(log'(x), 1(#()))
, log'(0(x)) -> if(ge(x, 1(#())), +(log'(x), 1(#())), #())}
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))
, +(1(x), 1(y)) -> 0(+(+(x, y), 1(#())))
, +(+(x, y), z) -> +(x, +(y, z))
, -(#(), x) -> #()
, -(x, #()) -> x
, -(0(x), 0(y)) -> 0(-(x, y))
, -(0(x), 1(y)) -> 1(-(-(x, y), 1(#())))
, -(1(x), 0(y)) -> 1(-(x, y))
, -(1(x), 1(y)) -> 0(-(x, y))
, not(true()) -> false()
, not(false()) -> true()
, if(true(), x, y) -> x
, if(false(), x, y) -> y
, ge(0(x), 0(y)) -> ge(x, y)
, ge(0(x), 1(y)) -> not(ge(y, x))
, ge(1(x), 0(y)) -> ge(x, y)
, ge(1(x), 1(y)) -> ge(x, y)
, ge(x, #()) -> true()
, ge(#(), 0(x)) -> ge(#(), x)
, ge(#(), 1(x)) -> false()
, log(x) -> -(log'(x), 1(#()))
, log'(#()) -> #()
, log'(1(x)) -> +(log'(x), 1(#()))
, log'(0(x)) -> if(ge(x, 1(#())), +(log'(x), 1(#())), #())}
Proof Output:
Computation stopped due to timeout after 60.0 seconds