details

property	value
status	complete
benchmark	quotminus.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	Rubio_04

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.0466471 seconds
cpu usage	0.041673
user time	0.021061
system time	0.020612
max virtual memory	113188.0
max residence set size	5576.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S X:S Y:S) (RULES min(min(X:S,Y:S),Z) -> min(X:S,plus(Y:S,Z)) min(s(X:S),s(Y:S)) -> min(X:S,Y:S) min(X:S,0) -> X:S plus(0,Y:S) -> Y:S plus(s(X:S),Y:S) -> s(plus(X:S,Y:S)) quot(0,s(Y:S)) -> 0 quot(s(X:S),s(Y:S)) -> s(quot(min(X:S,Y:S),s(Y:S))) ) Problem 1: Dependency Pairs Processor: -> Pairs: MIN(min(X:S,Y:S),Z) -> MIN(X:S,plus(Y:S,Z)) MIN(min(X:S,Y:S),Z) -> PLUS(Y:S,Z) MIN(s(X:S),s(Y:S)) -> MIN(X:S,Y:S) PLUS(s(X:S),Y:S) -> PLUS(X:S,Y:S) QUOT(s(X:S),s(Y:S)) -> MIN(X:S,Y:S) QUOT(s(X:S),s(Y:S)) -> QUOT(min(X:S,Y:S),s(Y:S)) -> Rules: min(min(X:S,Y:S),Z) -> min(X:S,plus(Y:S,Z)) min(s(X:S),s(Y:S)) -> min(X:S,Y:S) min(X:S,0) -> X:S plus(0,Y:S) -> Y:S plus(s(X:S),Y:S) -> s(plus(X:S,Y:S)) quot(0,s(Y:S)) -> 0 quot(s(X:S),s(Y:S)) -> s(quot(min(X:S,Y:S),s(Y:S))) Problem 1: SCC Processor: -> Pairs: MIN(min(X:S,Y:S),Z) -> MIN(X:S,plus(Y:S,Z)) MIN(min(X:S,Y:S),Z) -> PLUS(Y:S,Z) MIN(s(X:S),s(Y:S)) -> MIN(X:S,Y:S) PLUS(s(X:S),Y:S) -> PLUS(X:S,Y:S) QUOT(s(X:S),s(Y:S)) -> MIN(X:S,Y:S) QUOT(s(X:S),s(Y:S)) -> QUOT(min(X:S,Y:S),s(Y:S)) -> Rules: min(min(X:S,Y:S),Z) -> min(X:S,plus(Y:S,Z)) min(s(X:S),s(Y:S)) -> min(X:S,Y:S) min(X:S,0) -> X:S plus(0,Y:S) -> Y:S plus(s(X:S),Y:S) -> s(plus(X:S,Y:S)) quot(0,s(Y:S)) -> 0 quot(s(X:S),s(Y:S)) -> s(quot(min(X:S,Y:S),s(Y:S))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: PLUS(s(X:S),Y:S) -> PLUS(X:S,Y:S) ->->-> Rules: min(min(X:S,Y:S),Z) -> min(X:S,plus(Y:S,Z)) min(s(X:S),s(Y:S)) -> min(X:S,Y:S) min(X:S,0) -> X:S plus(0,Y:S) -> Y:S plus(s(X:S),Y:S) -> s(plus(X:S,Y:S)) quot(0,s(Y:S)) -> 0 quot(s(X:S),s(Y:S)) -> s(quot(min(X:S,Y:S),s(Y:S))) ->->Cycle: ->->-> Pairs: MIN(min(X:S,Y:S),Z) -> MIN(X:S,plus(Y:S,Z)) MIN(s(X:S),s(Y:S)) -> MIN(X:S,Y:S) ->->-> Rules: min(min(X:S,Y:S),Z) -> min(X:S,plus(Y:S,Z)) min(s(X:S),s(Y:S)) -> min(X:S,Y:S) min(X:S,0) -> X:S plus(0,Y:S) -> Y:S plus(s(X:S),Y:S) -> s(plus(X:S,Y:S)) quot(0,s(Y:S)) -> 0 quot(s(X:S),s(Y:S)) -> s(quot(min(X:S,Y:S),s(Y:S))) ->->Cycle: ->->-> Pairs: QUOT(s(X:S),s(Y:S)) -> QUOT(min(X:S,Y:S),s(Y:S)) ->->-> Rules: min(min(X:S,Y:S),Z) -> min(X:S,plus(Y:S,Z)) min(s(X:S),s(Y:S)) -> min(X:S,Y:S) min(X:S,0) -> X:S plus(0,Y:S) -> Y:S plus(s(X:S),Y:S) -> s(plus(X:S,Y:S)) quot(0,s(Y:S)) -> 0 quot(s(X:S),s(Y:S)) -> s(quot(min(X:S,Y:S),s(Y:S))) The problem is decomposed in 3 subproblems. Problem 1.1: Subterm Processor: -> Pairs: PLUS(s(X:S),Y:S) -> PLUS(X:S,Y:S) -> Rules: min(min(X:S,Y:S),Z) -> min(X:S,plus(Y:S,Z)) min(s(X:S),s(Y:S)) -> min(X:S,Y:S) min(X:S,0) -> X:S popout

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