details

property	value
status	complete
benchmark	rta1.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n179.star.cs.uiowa.edu
space	AProVE_04

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.0560099 seconds
cpu usage	0.039627
user time	0.023292
system time	0.016335
max virtual memory	113188.0
max residence set size	5684.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES ack(0,y:S) -> s(y:S) ack(s(x:S),0) -> ack(x:S,s(0)) ack(s(x:S),s(y:S)) -> ack(x:S,plus(y:S,ack(s(x:S),y:S))) plus(0,y:S) -> y:S plus(s(0),y:S) -> s(y:S) plus(s(s(x:S)),y:S) -> s(plus(x:S,s(y:S))) plus(x:S,s(s(y:S))) -> s(plus(s(x:S),y:S)) ) Problem 1: Dependency Pairs Processor: -> Pairs: ACK(s(x:S),0) -> ACK(x:S,s(0)) ACK(s(x:S),s(y:S)) -> ACK(s(x:S),y:S) ACK(s(x:S),s(y:S)) -> ACK(x:S,plus(y:S,ack(s(x:S),y:S))) ACK(s(x:S),s(y:S)) -> PLUS(y:S,ack(s(x:S),y:S)) PLUS(s(s(x:S)),y:S) -> PLUS(x:S,s(y:S)) PLUS(x:S,s(s(y:S))) -> PLUS(s(x:S),y:S) -> Rules: ack(0,y:S) -> s(y:S) ack(s(x:S),0) -> ack(x:S,s(0)) ack(s(x:S),s(y:S)) -> ack(x:S,plus(y:S,ack(s(x:S),y:S))) plus(0,y:S) -> y:S plus(s(0),y:S) -> s(y:S) plus(s(s(x:S)),y:S) -> s(plus(x:S,s(y:S))) plus(x:S,s(s(y:S))) -> s(plus(s(x:S),y:S)) Problem 1: SCC Processor: -> Pairs: ACK(s(x:S),0) -> ACK(x:S,s(0)) ACK(s(x:S),s(y:S)) -> ACK(s(x:S),y:S) ACK(s(x:S),s(y:S)) -> ACK(x:S,plus(y:S,ack(s(x:S),y:S))) ACK(s(x:S),s(y:S)) -> PLUS(y:S,ack(s(x:S),y:S)) PLUS(s(s(x:S)),y:S) -> PLUS(x:S,s(y:S)) PLUS(x:S,s(s(y:S))) -> PLUS(s(x:S),y:S) -> Rules: ack(0,y:S) -> s(y:S) ack(s(x:S),0) -> ack(x:S,s(0)) ack(s(x:S),s(y:S)) -> ack(x:S,plus(y:S,ack(s(x:S),y:S))) plus(0,y:S) -> y:S plus(s(0),y:S) -> s(y:S) plus(s(s(x:S)),y:S) -> s(plus(x:S,s(y:S))) plus(x:S,s(s(y:S))) -> s(plus(s(x:S),y:S)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: PLUS(s(s(x:S)),y:S) -> PLUS(x:S,s(y:S)) PLUS(x:S,s(s(y:S))) -> PLUS(s(x:S),y:S) ->->-> Rules: ack(0,y:S) -> s(y:S) ack(s(x:S),0) -> ack(x:S,s(0)) ack(s(x:S),s(y:S)) -> ack(x:S,plus(y:S,ack(s(x:S),y:S))) plus(0,y:S) -> y:S plus(s(0),y:S) -> s(y:S) plus(s(s(x:S)),y:S) -> s(plus(x:S,s(y:S))) plus(x:S,s(s(y:S))) -> s(plus(s(x:S),y:S)) ->->Cycle: ->->-> Pairs: ACK(s(x:S),0) -> ACK(x:S,s(0)) ACK(s(x:S),s(y:S)) -> ACK(s(x:S),y:S) ACK(s(x:S),s(y:S)) -> ACK(x:S,plus(y:S,ack(s(x:S),y:S))) ->->-> Rules: ack(0,y:S) -> s(y:S) ack(s(x:S),0) -> ack(x:S,s(0)) ack(s(x:S),s(y:S)) -> ack(x:S,plus(y:S,ack(s(x:S),y:S))) plus(0,y:S) -> y:S plus(s(0),y:S) -> s(y:S) plus(s(s(x:S)),y:S) -> s(plus(x:S,s(y:S))) plus(x:S,s(s(y:S))) -> s(plus(s(x:S),y:S)) The problem is decomposed in 2 subproblems. Problem 1.1: Reduction Pair Processor: -> Pairs: PLUS(s(s(x:S)),y:S) -> PLUS(x:S,s(y:S)) PLUS(x:S,s(s(y:S))) -> PLUS(s(x:S),y:S) -> Rules: ack(0,y:S) -> s(y:S) ack(s(x:S),0) -> ack(x:S,s(0)) ack(s(x:S),s(y:S)) -> ack(x:S,plus(y:S,ack(s(x:S),y:S))) plus(0,y:S) -> y:S plus(s(0),y:S) -> s(y:S) plus(s(s(x:S)),y:S) -> s(plus(x:S,s(y:S))) plus(x:S,s(s(y:S))) -> s(plus(s(x:S),y:S)) -> Usable rules: Empty ->Interpretation type: Linear popout

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