details

property	value
status	complete
benchmark	division.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n070.star.cs.uiowa.edu
space	Rubio_04

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.054666 seconds
cpu usage	0.045722
user time	0.024573
system time	0.021149
max virtual memory	113188.0
max residence set size	5708.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S X:S Y:S) (RULES ifMinus(ffalse,s(X:S),Y:S) -> s(minus(X:S,Y:S)) ifMinus(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) minus(0,Y:S) -> 0 minus(s(X:S),Y:S) -> ifMinus(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: ifMinus(ffalse,s(X:S),Y:S) -> s(minus(X:S,Y:S)) ifMinus(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) minus(0,Y:S) -> 0 minus(s(X:S),Y:S) -> ifMinus(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: IFMINUS(ffalse,s(X:S),Y:S) -> MINUS(X:S,Y:S) LE(s(X:S),s(Y:S)) -> LE(X:S,Y:S) MINUS(s(X:S),Y:S) -> IFMINUS(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: ifMinus(ffalse,s(X:S),Y:S) -> s(minus(X:S,Y:S)) ifMinus(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) minus(0,Y:S) -> 0 minus(s(X:S),Y:S) -> ifMinus(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: IFMINUS(ffalse,s(X:S),Y:S) -> MINUS(X:S,Y:S) LE(s(X:S),s(Y:S)) -> LE(X:S,Y:S) MINUS(s(X:S),Y:S) -> IFMINUS(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: ifMinus(ffalse,s(X:S),Y:S) -> s(minus(X:S,Y:S)) ifMinus(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) minus(0,Y:S) -> 0 minus(s(X:S),Y:S) -> ifMinus(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: ifMinus(ffalse,s(X:S),Y:S) -> s(minus(X:S,Y:S)) ifMinus(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) minus(0,Y:S) -> 0 minus(s(X:S),Y:S) -> ifMinus(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))) ->->Cycle: ->->-> Pairs: IFMINUS(ffalse,s(X:S),Y:S) -> MINUS(X:S,Y:S) MINUS(s(X:S),Y:S) -> IFMINUS(le(s(X:S),Y:S),s(X:S),Y:S) ->->-> Rules: ifMinus(ffalse,s(X:S),Y:S) -> s(minus(X:S,Y:S)) ifMinus(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) minus(0,Y:S) -> 0 minus(s(X:S),Y:S) -> ifMinus(le(s(X:S),Y:S),s(X:S),Y:S) popout

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