details

property	value
status	complete
benchmark	#4.29.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n054.star.cs.uiowa.edu
space	Strategy_removed_AG01

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.178593873978 seconds
cpu usage	0.129705721
max memory	4177920.0

stage attributes

key	value
output-size	12303
starexec-result	"YES"

output

/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES even(0) -> ttrue even(s(0)) -> ffalse even(s(s(x:S))) -> even(x:S) half(0) -> 0 half(s(s(x:S))) -> s(half(x:S)) if_times(ffalse,s(x:S),y:S) -> plus(y:S,times(x:S,y:S)) if_times(ttrue,s(x:S),y:S) -> plus(times(half(s(x:S)),y:S),times(half(s(x:S)),y:S)) plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) times(0,y:S) -> 0 times(s(x:S),y:S) -> if_times(even(s(x:S)),s(x:S),y:S) ) Problem 1: Innermost Equivalent Processor: -> Rules: even(0) -> ttrue even(s(0)) -> ffalse even(s(s(x:S))) -> even(x:S) half(0) -> 0 half(s(s(x:S))) -> s(half(x:S)) if_times(ffalse,s(x:S),y:S) -> plus(y:S,times(x:S,y:S)) if_times(ttrue,s(x:S),y:S) -> plus(times(half(s(x:S)),y:S),times(half(s(x:S)),y:S)) plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) times(0,y:S) -> 0 times(s(x:S),y:S) -> if_times(even(s(x:S)),s(x: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: EVEN(s(s(x:S))) -> EVEN(x:S) HALF(s(s(x:S))) -> HALF(x:S) IF_TIMES(ffalse,s(x:S),y:S) -> PLUS(y:S,times(x:S,y:S)) IF_TIMES(ffalse,s(x:S),y:S) -> TIMES(x:S,y:S) IF_TIMES(ttrue,s(x:S),y:S) -> HALF(s(x:S)) IF_TIMES(ttrue,s(x:S),y:S) -> PLUS(times(half(s(x:S)),y:S),times(half(s(x:S)),y:S)) IF_TIMES(ttrue,s(x:S),y:S) -> TIMES(half(s(x:S)),y:S) PLUS(s(x:S),y:S) -> PLUS(x:S,y:S) TIMES(s(x:S),y:S) -> EVEN(s(x:S)) TIMES(s(x:S),y:S) -> IF_TIMES(even(s(x:S)),s(x:S),y:S) -> Rules: even(0) -> ttrue even(s(0)) -> ffalse even(s(s(x:S))) -> even(x:S) half(0) -> 0 half(s(s(x:S))) -> s(half(x:S)) if_times(ffalse,s(x:S),y:S) -> plus(y:S,times(x:S,y:S)) if_times(ttrue,s(x:S),y:S) -> plus(times(half(s(x:S)),y:S),times(half(s(x:S)),y:S)) plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) times(0,y:S) -> 0 times(s(x:S),y:S) -> if_times(even(s(x:S)),s(x:S),y:S) Problem 1: SCC Processor: -> Pairs: EVEN(s(s(x:S))) -> EVEN(x:S) HALF(s(s(x:S))) -> HALF(x:S) IF_TIMES(ffalse,s(x:S),y:S) -> PLUS(y:S,times(x:S,y:S)) IF_TIMES(ffalse,s(x:S),y:S) -> TIMES(x:S,y:S) IF_TIMES(ttrue,s(x:S),y:S) -> HALF(s(x:S)) IF_TIMES(ttrue,s(x:S),y:S) -> PLUS(times(half(s(x:S)),y:S),times(half(s(x:S)),y:S)) IF_TIMES(ttrue,s(x:S),y:S) -> TIMES(half(s(x:S)),y:S) PLUS(s(x:S),y:S) -> PLUS(x:S,y:S) TIMES(s(x:S),y:S) -> EVEN(s(x:S)) TIMES(s(x:S),y:S) -> IF_TIMES(even(s(x:S)),s(x:S),y:S) -> Rules: even(0) -> ttrue even(s(0)) -> ffalse even(s(s(x:S))) -> even(x:S) half(0) -> 0 half(s(s(x:S))) -> s(half(x:S)) if_times(ffalse,s(x:S),y:S) -> plus(y:S,times(x:S,y:S)) if_times(ttrue,s(x:S),y:S) -> plus(times(half(s(x:S)),y:S),times(half(s(x:S)),y:S)) plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) times(0,y:S) -> 0 times(s(x:S),y:S) -> if_times(even(s(x:S)),s(x:S),y:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: PLUS(s(x:S),y:S) -> PLUS(x:S,y:S) popout

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