details

property	value
status	complete
benchmark	#4.30b.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n071.star.cs.uiowa.edu
space	Strategy_removed_AG01

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	81.9924 seconds
cpu usage	81.8632
user time	73.3987
system time	8.46448
max virtual memory	708824.0
max residence set size	6676.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES if_mod(ffalse,s(x:S),s(y:S)) -> s(x:S) if_mod(ttrue,x:S,y:S) -> mod(minus(x:S,y:S),y:S) le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S mod(0,y:S) -> 0 mod(s(x:S),0) -> 0 mod(s(x:S),s(y:S)) -> if_mod(le(y:S,x:S),s(x:S),s(y:S)) ) Problem 1: Innermost Equivalent Processor: -> Rules: if_mod(ffalse,s(x:S),s(y:S)) -> s(x:S) if_mod(ttrue,x:S,y:S) -> mod(minus(x:S,y:S),y:S) le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S mod(0,y:S) -> 0 mod(s(x:S),0) -> 0 mod(s(x:S),s(y:S)) -> if_mod(le(y:S,x:S),s(x:S),s(y:S)) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: IF_MOD(ttrue,x:S,y:S) -> MINUS(x:S,y:S) IF_MOD(ttrue,x:S,y:S) -> MOD(minus(x:S,y:S),y:S) LE(s(x:S),s(y:S)) -> LE(x:S,y:S) MINUS(s(x:S),s(y:S)) -> MINUS(x:S,y:S) MOD(s(x:S),s(y:S)) -> IF_MOD(le(y:S,x:S),s(x:S),s(y:S)) MOD(s(x:S),s(y:S)) -> LE(y:S,x:S) -> Rules: if_mod(ffalse,s(x:S),s(y:S)) -> s(x:S) if_mod(ttrue,x:S,y:S) -> mod(minus(x:S,y:S),y:S) le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S mod(0,y:S) -> 0 mod(s(x:S),0) -> 0 mod(s(x:S),s(y:S)) -> if_mod(le(y:S,x:S),s(x:S),s(y:S)) Problem 1: SCC Processor: -> Pairs: IF_MOD(ttrue,x:S,y:S) -> MINUS(x:S,y:S) IF_MOD(ttrue,x:S,y:S) -> MOD(minus(x:S,y:S),y:S) LE(s(x:S),s(y:S)) -> LE(x:S,y:S) MINUS(s(x:S),s(y:S)) -> MINUS(x:S,y:S) MOD(s(x:S),s(y:S)) -> IF_MOD(le(y:S,x:S),s(x:S),s(y:S)) MOD(s(x:S),s(y:S)) -> LE(y:S,x:S) -> Rules: if_mod(ffalse,s(x:S),s(y:S)) -> s(x:S) if_mod(ttrue,x:S,y:S) -> mod(minus(x:S,y:S),y:S) le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S mod(0,y:S) -> 0 mod(s(x:S),0) -> 0 mod(s(x:S),s(y:S)) -> if_mod(le(y:S,x:S),s(x:S),s(y:S)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: MINUS(s(x:S),s(y:S)) -> MINUS(x:S,y:S) ->->-> Rules: if_mod(ffalse,s(x:S),s(y:S)) -> s(x:S) if_mod(ttrue,x:S,y:S) -> mod(minus(x:S,y:S),y:S) le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S mod(0,y:S) -> 0 mod(s(x:S),0) -> 0 mod(s(x:S),s(y:S)) -> if_mod(le(y:S,x:S),s(x:S),s(y:S)) ->->Cycle: ->->-> Pairs: LE(s(x:S),s(y:S)) -> LE(x:S,y:S) ->->-> Rules: if_mod(ffalse,s(x:S),s(y:S)) -> s(x:S) if_mod(ttrue,x:S,y:S) -> mod(minus(x:S,y:S),y:S) le(0,y:S) -> ttrue popout

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