details

property	value
status	complete
benchmark	AC51.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	AProVE_AC_04

run statistics

property	value
solver	muterm 5.18
configuration	default
runtime (wallclock)	0.601855 seconds
cpu usage	0.57022
user time	0.357086
system time	0.213134
max virtual memory	677248.0
max residence set size	5912.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR x y) (THEORY (AC plus)) (RULES plus(0,y) -> y plus(s(x),0) -> s(x) plus(s(x),s(y)) -> s(plus(s(x),plus(y,0))) ) Problem 1: Dependency Pairs Processor: -> FAxioms: PLUS(plus(x2,x3),x4) = PLUS(x2,plus(x3,x4)) PLUS(x2,x3) = PLUS(x3,x2) -> Pairs: PLUS(plus(0,y),x2) -> PLUS(y,x2) PLUS(plus(s(x),0),x2) -> PLUS(s(x),x2) PLUS(plus(s(x),s(y)),x2) -> PLUS(s(plus(s(x),plus(y,0))),x2) PLUS(plus(s(x),s(y)),x2) -> PLUS(s(x),plus(y,0)) PLUS(plus(s(x),s(y)),x2) -> PLUS(y,0) PLUS(s(x),s(y)) -> PLUS(s(x),plus(y,0)) PLUS(s(x),s(y)) -> PLUS(y,0) -> EAxioms: plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4)) plus(x2,x3) = plus(x3,x2) -> Rules: plus(0,y) -> y plus(s(x),0) -> s(x) plus(s(x),s(y)) -> s(plus(s(x),plus(y,0))) -> SRules: PLUS(plus(x2,x3),x4) -> PLUS(x2,x3) PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4) Problem 1: SCC Processor: -> FAxioms: PLUS(plus(x2,x3),x4) = PLUS(x2,plus(x3,x4)) PLUS(x2,x3) = PLUS(x3,x2) -> Pairs: PLUS(plus(0,y),x2) -> PLUS(y,x2) PLUS(plus(s(x),0),x2) -> PLUS(s(x),x2) PLUS(plus(s(x),s(y)),x2) -> PLUS(s(plus(s(x),plus(y,0))),x2) PLUS(plus(s(x),s(y)),x2) -> PLUS(s(x),plus(y,0)) PLUS(plus(s(x),s(y)),x2) -> PLUS(y,0) PLUS(s(x),s(y)) -> PLUS(s(x),plus(y,0)) PLUS(s(x),s(y)) -> PLUS(y,0) -> EAxioms: plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4)) plus(x2,x3) = plus(x3,x2) -> Rules: plus(0,y) -> y plus(s(x),0) -> s(x) plus(s(x),s(y)) -> s(plus(s(x),plus(y,0))) -> SRules: PLUS(plus(x2,x3),x4) -> PLUS(x2,x3) PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: PLUS(plus(0,y),x2) -> PLUS(y,x2) PLUS(plus(s(x),0),x2) -> PLUS(s(x),x2) PLUS(plus(s(x),s(y)),x2) -> PLUS(s(plus(s(x),plus(y,0))),x2) PLUS(plus(s(x),s(y)),x2) -> PLUS(s(x),plus(y,0)) PLUS(plus(s(x),s(y)),x2) -> PLUS(y,0) PLUS(s(x),s(y)) -> PLUS(s(x),plus(y,0)) PLUS(s(x),s(y)) -> PLUS(y,0) -> FAxioms: plus(plus(x2,x3),x4) -> plus(x2,plus(x3,x4)) plus(x2,x3) -> plus(x3,x2) PLUS(plus(x2,x3),x4) -> PLUS(x2,plus(x3,x4)) PLUS(x2,x3) -> PLUS(x3,x2) -> EAxioms: plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4)) plus(x2,x3) = plus(x3,x2) ->->-> Rules: plus(0,y) -> y plus(s(x),0) -> s(x) plus(s(x),s(y)) -> s(plus(s(x),plus(y,0))) -> SRules: PLUS(plus(x2,x3),x4) -> PLUS(x2,x3) PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4) Problem 1: Reduction Pairs Processor: -> FAxioms: PLUS(plus(x2,x3),x4) = PLUS(x2,plus(x3,x4)) PLUS(x2,x3) = PLUS(x3,x2) -> Pairs: PLUS(plus(0,y),x2) -> PLUS(y,x2) PLUS(plus(s(x),0),x2) -> PLUS(s(x),x2) PLUS(plus(s(x),s(y)),x2) -> PLUS(s(plus(s(x),plus(y,0))),x2) PLUS(plus(s(x),s(y)),x2) -> PLUS(s(x),plus(y,0)) PLUS(plus(s(x),s(y)),x2) -> PLUS(y,0) popout

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all output return to TRS Equational