details

property	value
status	complete
benchmark	#3.8b.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n180.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.0735719 seconds
cpu usage	0.07714
user time	0.046957
system time	0.030183
max virtual memory	113188.0
max residence set size	5980.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES if_minus(ffalse,s(x:S),y:S) -> s(minus(x:S,y:S)) if_minus(ttrue,s(x:S),y:S) -> 0 le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) log(s(0)) -> 0 log(s(s(x:S))) -> s(log(s(quot(x:S,s(s(0)))))) minus(0,y:S) -> 0 minus(s(x:S),y:S) -> if_minus(le(s(x:S),y:S),s(x:S),y:S) quot(0,s(y:S)) -> 0 quot(s(x:S),s(y:S)) -> s(quot(minus(x:S,y:S),s(y:S))) ) Problem 1: Innermost Equivalent Processor: -> Rules: if_minus(ffalse,s(x:S),y:S) -> s(minus(x:S,y:S)) if_minus(ttrue,s(x:S),y:S) -> 0 le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) log(s(0)) -> 0 log(s(s(x:S))) -> s(log(s(quot(x:S,s(s(0)))))) minus(0,y:S) -> 0 minus(s(x:S),y:S) -> if_minus(le(s(x:S),y:S),s(x:S),y:S) quot(0,s(y:S)) -> 0 quot(s(x:S),s(y:S)) -> s(quot(minus(x:S,y: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_MINUS(ffalse,s(x:S),y:S) -> MINUS(x:S,y:S) LE(s(x:S),s(y:S)) -> LE(x:S,y:S) LOG(s(s(x:S))) -> LOG(s(quot(x:S,s(s(0))))) LOG(s(s(x:S))) -> QUOT(x:S,s(s(0))) MINUS(s(x:S),y:S) -> IF_MINUS(le(s(x:S),y:S),s(x:S),y:S) MINUS(s(x:S),y:S) -> LE(s(x:S),y:S) QUOT(s(x:S),s(y:S)) -> MINUS(x:S,y:S) QUOT(s(x:S),s(y:S)) -> QUOT(minus(x:S,y:S),s(y:S)) -> Rules: if_minus(ffalse,s(x:S),y:S) -> s(minus(x:S,y:S)) if_minus(ttrue,s(x:S),y:S) -> 0 le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) log(s(0)) -> 0 log(s(s(x:S))) -> s(log(s(quot(x:S,s(s(0)))))) minus(0,y:S) -> 0 minus(s(x:S),y:S) -> if_minus(le(s(x:S),y:S),s(x:S),y:S) quot(0,s(y:S)) -> 0 quot(s(x:S),s(y:S)) -> s(quot(minus(x:S,y:S),s(y:S))) Problem 1: SCC Processor: -> Pairs: IF_MINUS(ffalse,s(x:S),y:S) -> MINUS(x:S,y:S) LE(s(x:S),s(y:S)) -> LE(x:S,y:S) LOG(s(s(x:S))) -> LOG(s(quot(x:S,s(s(0))))) LOG(s(s(x:S))) -> QUOT(x:S,s(s(0))) MINUS(s(x:S),y:S) -> IF_MINUS(le(s(x:S),y:S),s(x:S),y:S) MINUS(s(x:S),y:S) -> LE(s(x:S),y:S) QUOT(s(x:S),s(y:S)) -> MINUS(x:S,y:S) QUOT(s(x:S),s(y:S)) -> QUOT(minus(x:S,y:S),s(y:S)) -> Rules: if_minus(ffalse,s(x:S),y:S) -> s(minus(x:S,y:S)) if_minus(ttrue,s(x:S),y:S) -> 0 le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) log(s(0)) -> 0 log(s(s(x:S))) -> s(log(s(quot(x:S,s(s(0)))))) minus(0,y:S) -> 0 minus(s(x:S),y:S) -> if_minus(le(s(x:S),y:S),s(x:S),y:S) quot(0,s(y:S)) -> 0 quot(s(x:S),s(y:S)) -> s(quot(minus(x:S,y:S),s(y:S))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: LE(s(x:S),s(y:S)) -> LE(x:S,y:S) ->->-> Rules: if_minus(ffalse,s(x:S),y:S) -> s(minus(x:S,y:S)) if_minus(ttrue,s(x:S),y:S) -> 0 le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) log(s(0)) -> 0 log(s(s(x:S))) -> s(log(s(quot(x:S,s(s(0)))))) minus(0,y:S) -> 0 minus(s(x:S),y:S) -> if_minus(le(s(x:S),y:S),s(x:S),y:S) popout

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