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TRS Stand 20472 pair #381712416
details
property
value
status
complete
benchmark
#4.23.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n005.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.0356841087341 seconds
cpu usage
0.030779049
max memory
3457024.0
stage attributes
key
value
output-size
4243
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR x y z) (RULES plus(0,y) -> y plus(s(x),y) -> s(plus(x,y)) quot(0,s(y),s(z)) -> 0 quot(s(x),s(y),z) -> quot(x,y,z) quot(x,0,s(z)) -> s(quot(x,plus(z,s(0)),s(z))) ) Problem 1: Innermost Equivalent Processor: -> Rules: plus(0,y) -> y plus(s(x),y) -> s(plus(x,y)) quot(0,s(y),s(z)) -> 0 quot(s(x),s(y),z) -> quot(x,y,z) quot(x,0,s(z)) -> s(quot(x,plus(z,s(0)),s(z))) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: PLUS(s(x),y) -> PLUS(x,y) QUOT(s(x),s(y),z) -> QUOT(x,y,z) QUOT(x,0,s(z)) -> PLUS(z,s(0)) QUOT(x,0,s(z)) -> QUOT(x,plus(z,s(0)),s(z)) -> Rules: plus(0,y) -> y plus(s(x),y) -> s(plus(x,y)) quot(0,s(y),s(z)) -> 0 quot(s(x),s(y),z) -> quot(x,y,z) quot(x,0,s(z)) -> s(quot(x,plus(z,s(0)),s(z))) Problem 1: SCC Processor: -> Pairs: PLUS(s(x),y) -> PLUS(x,y) QUOT(s(x),s(y),z) -> QUOT(x,y,z) QUOT(x,0,s(z)) -> PLUS(z,s(0)) QUOT(x,0,s(z)) -> QUOT(x,plus(z,s(0)),s(z)) -> Rules: plus(0,y) -> y plus(s(x),y) -> s(plus(x,y)) quot(0,s(y),s(z)) -> 0 quot(s(x),s(y),z) -> quot(x,y,z) quot(x,0,s(z)) -> s(quot(x,plus(z,s(0)),s(z))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: PLUS(s(x),y) -> PLUS(x,y) ->->-> Rules: plus(0,y) -> y plus(s(x),y) -> s(plus(x,y)) quot(0,s(y),s(z)) -> 0 quot(s(x),s(y),z) -> quot(x,y,z) quot(x,0,s(z)) -> s(quot(x,plus(z,s(0)),s(z))) ->->Cycle: ->->-> Pairs: QUOT(s(x),s(y),z) -> QUOT(x,y,z) QUOT(x,0,s(z)) -> QUOT(x,plus(z,s(0)),s(z)) ->->-> Rules: plus(0,y) -> y plus(s(x),y) -> s(plus(x,y)) quot(0,s(y),s(z)) -> 0 quot(s(x),s(y),z) -> quot(x,y,z) quot(x,0,s(z)) -> s(quot(x,plus(z,s(0)),s(z))) The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: PLUS(s(x),y) -> PLUS(x,y) -> Rules: plus(0,y) -> y plus(s(x),y) -> s(plus(x,y)) quot(0,s(y),s(z)) -> 0 quot(s(x),s(y),z) -> quot(x,y,z) quot(x,0,s(z)) -> s(quot(x,plus(z,s(0)),s(z))) ->Projection: pi(PLUS) = 1 Problem 1.1:
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