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TRS Standard pair #487067729
details
property
value
status
complete
benchmark
2.17.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n174.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0160901 seconds
cpu usage
0.016583
user time
0.007904
system time
0.008679
max virtual memory
113188.0
max residence set size
4248.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S) (RULES sum(0) -> 0 sum(s(x:S)) -> +(sum(x:S),s(x:S)) sum1(0) -> 0 sum1(s(x:S)) -> s(+(sum1(x:S),+(x:S,x:S))) ) Problem 1: Innermost Equivalent Processor: -> Rules: sum(0) -> 0 sum(s(x:S)) -> +(sum(x:S),s(x:S)) sum1(0) -> 0 sum1(s(x:S)) -> s(+(sum1(x:S),+(x:S,x:S))) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: SUM(s(x:S)) -> SUM(x:S) SUM1(s(x:S)) -> SUM1(x:S) -> Rules: sum(0) -> 0 sum(s(x:S)) -> +(sum(x:S),s(x:S)) sum1(0) -> 0 sum1(s(x:S)) -> s(+(sum1(x:S),+(x:S,x:S))) Problem 1: SCC Processor: -> Pairs: SUM(s(x:S)) -> SUM(x:S) SUM1(s(x:S)) -> SUM1(x:S) -> Rules: sum(0) -> 0 sum(s(x:S)) -> +(sum(x:S),s(x:S)) sum1(0) -> 0 sum1(s(x:S)) -> s(+(sum1(x:S),+(x:S,x:S))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: SUM1(s(x:S)) -> SUM1(x:S) ->->-> Rules: sum(0) -> 0 sum(s(x:S)) -> +(sum(x:S),s(x:S)) sum1(0) -> 0 sum1(s(x:S)) -> s(+(sum1(x:S),+(x:S,x:S))) ->->Cycle: ->->-> Pairs: SUM(s(x:S)) -> SUM(x:S) ->->-> Rules: sum(0) -> 0 sum(s(x:S)) -> +(sum(x:S),s(x:S)) sum1(0) -> 0 sum1(s(x:S)) -> s(+(sum1(x:S),+(x:S,x:S))) The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: SUM1(s(x:S)) -> SUM1(x:S) -> Rules: sum(0) -> 0 sum(s(x:S)) -> +(sum(x:S),s(x:S)) sum1(0) -> 0 sum1(s(x:S)) -> s(+(sum1(x:S),+(x:S,x:S))) ->Projection: pi(SUM1) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: sum(0) -> 0 sum(s(x:S)) -> +(sum(x:S),s(x:S)) sum1(0) -> 0 sum1(s(x:S)) -> s(+(sum1(x:S),+(x:S,x:S))) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: Subterm Processor: -> Pairs: SUM(s(x:S)) -> SUM(x:S)
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