details

property	value
status	complete
benchmark	thiemann15.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n178.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.118627 seconds
cpu usage	0.101786
user time	0.054348
system time	0.047438
max virtual memory	113188.0
max residence set size	5696.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES bitIter(x:S,y:S) -> if(zero(x:S),x:S,inc(y:S)) bits(x:S) -> bitIter(x:S,0) half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) if(ffalse,x:S,y:S) -> bitIter(half(x:S),y:S) if(ttrue,x:S,y:S) -> p(y:S) inc(0) -> 0 inc(s(x:S)) -> s(inc(x:S)) p(0) -> 0 p(s(x:S)) -> x:S zero(0) -> ttrue zero(s(x:S)) -> ffalse ) Problem 1: Innermost Equivalent Processor: -> Rules: bitIter(x:S,y:S) -> if(zero(x:S),x:S,inc(y:S)) bits(x:S) -> bitIter(x:S,0) half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) if(ffalse,x:S,y:S) -> bitIter(half(x:S),y:S) if(ttrue,x:S,y:S) -> p(y:S) inc(0) -> 0 inc(s(x:S)) -> s(inc(x:S)) p(0) -> 0 p(s(x:S)) -> x:S zero(0) -> ttrue zero(s(x:S)) -> ffalse -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: BITITER(x:S,y:S) -> IF(zero(x:S),x:S,inc(y:S)) BITITER(x:S,y:S) -> INC(y:S) BITITER(x:S,y:S) -> ZERO(x:S) BITS(x:S) -> BITITER(x:S,0) HALF(s(s(x:S))) -> HALF(x:S) IF(ffalse,x:S,y:S) -> BITITER(half(x:S),y:S) IF(ffalse,x:S,y:S) -> HALF(x:S) IF(ttrue,x:S,y:S) -> P(y:S) INC(s(x:S)) -> INC(x:S) -> Rules: bitIter(x:S,y:S) -> if(zero(x:S),x:S,inc(y:S)) bits(x:S) -> bitIter(x:S,0) half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) if(ffalse,x:S,y:S) -> bitIter(half(x:S),y:S) if(ttrue,x:S,y:S) -> p(y:S) inc(0) -> 0 inc(s(x:S)) -> s(inc(x:S)) p(0) -> 0 p(s(x:S)) -> x:S zero(0) -> ttrue zero(s(x:S)) -> ffalse Problem 1: SCC Processor: -> Pairs: BITITER(x:S,y:S) -> IF(zero(x:S),x:S,inc(y:S)) BITITER(x:S,y:S) -> INC(y:S) BITITER(x:S,y:S) -> ZERO(x:S) BITS(x:S) -> BITITER(x:S,0) HALF(s(s(x:S))) -> HALF(x:S) IF(ffalse,x:S,y:S) -> BITITER(half(x:S),y:S) IF(ffalse,x:S,y:S) -> HALF(x:S) IF(ttrue,x:S,y:S) -> P(y:S) INC(s(x:S)) -> INC(x:S) -> Rules: bitIter(x:S,y:S) -> if(zero(x:S),x:S,inc(y:S)) bits(x:S) -> bitIter(x:S,0) half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) if(ffalse,x:S,y:S) -> bitIter(half(x:S),y:S) if(ttrue,x:S,y:S) -> p(y:S) inc(0) -> 0 inc(s(x:S)) -> s(inc(x:S)) p(0) -> 0 p(s(x:S)) -> x:S zero(0) -> ttrue zero(s(x:S)) -> ffalse ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: INC(s(x:S)) -> INC(x:S) popout

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