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TRS Standard pair #487069212
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
n181.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
0.580565 seconds
cpu usage
1.15878
user time
0.893537
system time
0.265241
max virtual memory
2131784.0
max residence set size
68676.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: plus(0(),Y) -> Y plus(s(X),Y) -> s(plus(X,Y)) min(X,0()) -> X min(s(X),s(Y)) -> min(X,Y) min(min(X,Y),Z()) -> min(X,plus(Y,Z())) quot(0(),s(Y)) -> 0() quot(s(X),s(Y)) -> s(quot(min(X,Y),s(Y))) Proof: DP Processor: DPs: plus#(s(X),Y) -> plus#(X,Y) min#(s(X),s(Y)) -> min#(X,Y) min#(min(X,Y),Z()) -> plus#(Y,Z()) min#(min(X,Y),Z()) -> min#(X,plus(Y,Z())) quot#(s(X),s(Y)) -> min#(X,Y) quot#(s(X),s(Y)) -> quot#(min(X,Y),s(Y)) TRS: plus(0(),Y) -> Y plus(s(X),Y) -> s(plus(X,Y)) min(X,0()) -> X min(s(X),s(Y)) -> min(X,Y) min(min(X,Y),Z()) -> min(X,plus(Y,Z())) quot(0(),s(Y)) -> 0() quot(s(X),s(Y)) -> s(quot(min(X,Y),s(Y))) TDG Processor: DPs: plus#(s(X),Y) -> plus#(X,Y) min#(s(X),s(Y)) -> min#(X,Y) min#(min(X,Y),Z()) -> plus#(Y,Z()) min#(min(X,Y),Z()) -> min#(X,plus(Y,Z())) quot#(s(X),s(Y)) -> min#(X,Y) quot#(s(X),s(Y)) -> quot#(min(X,Y),s(Y)) TRS: plus(0(),Y) -> Y plus(s(X),Y) -> s(plus(X,Y)) min(X,0()) -> X min(s(X),s(Y)) -> min(X,Y) min(min(X,Y),Z()) -> min(X,plus(Y,Z())) quot(0(),s(Y)) -> 0() quot(s(X),s(Y)) -> s(quot(min(X,Y),s(Y))) graph: quot#(s(X),s(Y)) -> quot#(min(X,Y),s(Y)) -> quot#(s(X),s(Y)) -> quot#(min(X,Y),s(Y)) quot#(s(X),s(Y)) -> quot#(min(X,Y),s(Y)) -> quot#(s(X),s(Y)) -> min#(X,Y) quot#(s(X),s(Y)) -> min#(X,Y) -> min#(min(X,Y),Z()) -> min#(X,plus(Y,Z())) quot#(s(X),s(Y)) -> min#(X,Y) -> min#(min(X,Y),Z()) -> plus#(Y,Z()) quot#(s(X),s(Y)) -> min#(X,Y) -> min#(s(X),s(Y)) -> min#(X,Y) min#(min(X,Y),Z()) -> min#(X,plus(Y,Z())) -> min#(min(X,Y),Z()) -> min#(X,plus(Y,Z())) min#(min(X,Y),Z()) -> min#(X,plus(Y,Z())) -> min#(min(X,Y),Z()) -> plus#(Y,Z()) min#(min(X,Y),Z()) -> min#(X,plus(Y,Z())) -> min#(s(X),s(Y)) -> min#(X,Y) min#(min(X,Y),Z()) -> plus#(Y,Z()) -> plus#(s(X),Y) -> plus#(X,Y) min#(s(X),s(Y)) -> min#(X,Y) -> min#(min(X,Y),Z()) -> min#(X,plus(Y,Z())) min#(s(X),s(Y)) -> min#(X,Y) -> min#(min(X,Y),Z()) -> plus#(Y,Z()) min#(s(X),s(Y)) -> min#(X,Y) -> min#(s(X),s(Y)) -> min#(X,Y) plus#(s(X),Y) -> plus#(X,Y) -> plus#(s(X),Y) -> plus#(X,Y) SCC Processor: #sccs: 3 #rules: 4 #arcs: 13/36 DPs: quot#(s(X),s(Y)) -> quot#(min(X,Y),s(Y)) TRS: plus(0(),Y) -> Y plus(s(X),Y) -> s(plus(X,Y)) min(X,0()) -> X min(s(X),s(Y)) -> min(X,Y) min(min(X,Y),Z()) -> min(X,plus(Y,Z())) quot(0(),s(Y)) -> 0() quot(s(X),s(Y)) -> s(quot(min(X,Y),s(Y))) Subterm Criterion Processor: simple projection: pi(min) = 0 pi(quot#) = 0 problem: DPs: TRS: plus(0(),Y) -> Y plus(s(X),Y) -> s(plus(X,Y)) min(X,0()) -> X min(s(X),s(Y)) -> min(X,Y) min(min(X,Y),Z()) -> min(X,plus(Y,Z())) quot(0(),s(Y)) -> 0() quot(s(X),s(Y)) -> s(quot(min(X,Y),s(Y))) Qed DPs: min#(s(X),s(Y)) -> min#(X,Y)
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