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TRS Standard pair #487066670
details
property
value
status
complete
benchmark
21.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n177.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
NTI-TC20-firstrun
configuration
Default 200
runtime (wallclock)
26.8557 seconds
cpu usage
105.451
user time
102.102
system time
3.34826
max virtual memory
3.5399512E7
max residence set size
9421388.0
stage attributes
key
value
starexec-result
YES
output
YES Prover = TRS(tech=GUIDED_UNF_TRIPLES, nb_unfoldings=unlimited, unfold_variables=false, max_nb_coefficients=12, max_nb_unfolded_rules=-1, strategy=LEFTMOST_NE) ** BEGIN proof argument ** All the DP problems were proved finite. As all the involved DP processors are sound, the TRS under analysis terminates. ** END proof argument ** ** BEGIN proof description ** ## Searching for a generalized rewrite rule (a rule whose right-hand side contains a variable that does not occur in the left-hand side)... No generalized rewrite rule found! ## Applying the DP framework... ## Round 1: ## DP problem: Dependency pairs = [+^#(+(_0,_1),_2) -> +^#(_0,+(_1,_2)), +^#(+(_0,_1),_2) -> +^#(_1,_2)] TRS = {+(p1,p1) -> p2, +(p1,+(p2,p2)) -> p5, +(p5,p5) -> p10, +(+(_0,_1),_2) -> +(_0,+(_1,_2)), +(p1,+(p1,_0)) -> +(p2,_0), +(p1,+(p2,+(p2,_0))) -> +(p5,_0), +(p2,p1) -> +(p1,p2), +(p2,+(p1,_0)) -> +(p1,+(p2,_0)), +(p2,+(p2,p2)) -> +(p1,p5), +(p2,+(p2,+(p2,_0))) -> +(p1,+(p5,_0)), +(p5,p1) -> +(p1,p5), +(p5,+(p1,_0)) -> +(p1,+(p5,_0)), +(p5,p2) -> +(p2,p5), +(p5,+(p2,_0)) -> +(p2,+(p5,_0)), +(p5,+(p5,_0)) -> +(p10,_0), +(p10,p1) -> +(p1,p10), +(p10,+(p1,_0)) -> +(p1,+(p10,_0)), +(p10,p2) -> +(p2,p10), +(p10,+(p2,_0)) -> +(p2,+(p10,_0)), +(p10,p5) -> +(p5,p10), +(p10,+(p5,_0)) -> +(p5,+(p10,_0))} ## Trying with homeomorphic embeddings... Failed! ## Trying with polynomial interpretations... The constraints are satisfied by the polynomials: {p1:[0], +(_0,_1):[1 + _0 + _1], p5:[0], p2:[0], p10:[0], +^#(_0,_1):[_0]} for all instantiations of the variables with values greater than or equal to mu = 0. This DP problem is finite. ## DP problem: Dependency pairs = [+^#(p1,+(p1,_0)) -> +^#(p2,_0), +^#(p2,+(p1,_0)) -> +^#(p1,+(p2,_0)), +^#(p2,+(p1,_0)) -> +^#(p2,_0), +^#(p5,+(p2,_0)) -> +^#(p2,+(p5,_0)), +^#(p1,+(p2,+(p2,_0))) -> +^#(p5,_0), +^#(p10,+(p1,_0)) -> +^#(p1,+(p10,_0)), +^#(p5,+(p1,_0)) -> +^#(p1,+(p5,_0)), +^#(p2,+(p2,+(p2,_0))) -> +^#(p1,+(p5,_0)), +^#(p10,+(p2,_0)) -> +^#(p2,+(p10,_0)), +^#(p5,+(p5,_0)) -> +^#(p10,_0), +^#(p5,+(p1,_0)) -> +^#(p5,_0), +^#(p5,+(p2,_0)) -> +^#(p5,_0), +^#(p10,+(p5,_0)) -> +^#(p5,+(p10,_0)), +^#(p10,+(p1,_0)) -> +^#(p10,_0), +^#(p10,+(p2,_0)) -> +^#(p10,_0), +^#(p10,+(p5,_0)) -> +^#(p10,_0), +^#(p2,+(p2,+(p2,_0))) -> +^#(p5,_0)] TRS = {+(p1,p1) -> p2, +(p1,+(p2,p2)) -> p5, +(p5,p5) -> p10, +(+(_0,_1),_2) -> +(_0,+(_1,_2)), +(p1,+(p1,_0)) -> +(p2,_0), +(p1,+(p2,+(p2,_0))) -> +(p5,_0), +(p2,p1) -> +(p1,p2), +(p2,+(p1,_0)) -> +(p1,+(p2,_0)), +(p2,+(p2,p2)) -> +(p1,p5), +(p2,+(p2,+(p2,_0))) -> +(p1,+(p5,_0)), +(p5,p1) -> +(p1,p5), +(p5,+(p1,_0)) -> +(p1,+(p5,_0)), +(p5,p2) -> +(p2,p5), +(p5,+(p2,_0)) -> +(p2,+(p5,_0)), +(p5,+(p5,_0)) -> +(p10,_0), +(p10,p1) -> +(p1,p10), +(p10,+(p1,_0)) -> +(p1,+(p10,_0)), +(p10,p2) -> +(p2,p10), +(p10,+(p2,_0)) -> +(p2,+(p10,_0)), +(p10,p5) -> +(p5,p10), +(p10,+(p5,_0)) -> +(p5,+(p10,_0))} ## Trying with homeomorphic embeddings... Failed! ## Trying with polynomial interpretations... Successfully decomposed the DP problem into smaller problems to solve! ## Round 2: ## DP problem: Dependency pairs = [+^#(p10,+(p5,_0)) -> +^#(p5,+(p10,_0)), +^#(p5,+(p5,_0)) -> +^#(p10,_0)] TRS = {+(p1,p1) -> p2, +(p1,+(p2,p2)) -> p5, +(p5,p5) -> p10, +(+(_0,_1),_2) -> +(_0,+(_1,_2)), +(p1,+(p1,_0)) -> +(p2,_0), +(p1,+(p2,+(p2,_0))) -> +(p5,_0), +(p2,p1) -> +(p1,p2), +(p2,+(p1,_0)) -> +(p1,+(p2,_0)), +(p2,+(p2,p2)) -> +(p1,p5), +(p2,+(p2,+(p2,_0))) -> +(p1,+(p5,_0)), +(p5,p1) -> +(p1,p5), +(p5,+(p1,_0)) -> +(p1,+(p5,_0)), +(p5,p2) -> +(p2,p5), +(p5,+(p2,_0)) -> +(p2,+(p5,_0)), +(p5,+(p5,_0)) -> +(p10,_0), +(p10,p1) -> +(p1,p10), +(p10,+(p1,_0)) -> +(p1,+(p10,_0)), +(p10,p2) -> +(p2,p10), +(p10,+(p2,_0)) -> +(p2,+(p10,_0)), +(p10,p5) -> +(p5,p10), +(p10,+(p5,_0)) -> +(p5,+(p10,_0))} ## Trying with homeomorphic embeddings... Failed! ## Trying with polynomial interpretations... The constraints are satisfied by the polynomials: {p1:[0], +(_0,_1):[1 + _0 + _1], p5:[1], p2:[0], p10:[0], +^#(_0,_1):[_0]} for all instantiations of the variables with values greater than or equal to mu = 0. This DP problem is finite. ## DP problem: Dependency pairs = [+^#(p10,+(p5,_0)) -> +^#(p5,+(p10,_0)), +^#(p5,+(p5,_0)) -> +^#(p10,_0)] TRS = {+(p1,p1) -> p2, +(p1,+(p2,p2)) -> p5, +(p5,p5) -> p10, +(+(_0,_1),_2) -> +(_0,+(_1,_2)), +(p1,+(p1,_0)) -> +(p2,_0), +(p1,+(p2,+(p2,_0))) -> +(p5,_0), +(p2,p1) -> +(p1,p2), +(p2,+(p1,_0)) -> +(p1,+(p2,_0)), +(p2,+(p2,p2)) -> +(p1,p5), +(p2,+(p2,+(p2,_0))) -> +(p1,+(p5,_0)), +(p5,p1) -> +(p1,p5), +(p5,+(p1,_0)) -> +(p1,+(p5,_0)), +(p5,p2) -> +(p2,p5), +(p5,+(p2,_0)) -> +(p2,+(p5,_0)), +(p5,+(p5,_0)) -> +(p10,_0), +(p10,p1) -> +(p1,p10), +(p10,+(p1,_0)) -> +(p1,+(p10,_0)), +(p10,p2) -> +(p2,p10), +(p10,+(p2,_0)) -> +(p2,+(p10,_0)), +(p10,p5) -> +(p5,p10), +(p10,+(p5,_0)) -> +(p5,+(p10,_0))} ## Trying with homeomorphic embeddings... Failed! ## Trying with polynomial interpretations... The constraints are satisfied by the polynomials: {p1:[0], +(_0,_1):[1 + _0 + _1], p5:[1], p2:[0], p10:[0], +^#(_0,_1):[_0]} for all instantiations of the variables with values greater than or equal to mu = 0. This DP problem is finite. ## DP problem: Dependency pairs = [+^#(p10,+(p5,_0)) -> +^#(p5,+(p10,_0)), +^#(p5,+(p5,_0)) -> +^#(p10,_0)] TRS = {+(p1,p1) -> p2, +(p1,+(p2,p2)) -> p5, +(p5,p5) -> p10, +(+(_0,_1),_2) -> +(_0,+(_1,_2)), +(p1,+(p1,_0)) -> +(p2,_0), +(p1,+(p2,+(p2,_0))) -> +(p5,_0), +(p2,p1) -> +(p1,p2), +(p2,+(p1,_0)) -> +(p1,+(p2,_0)), +(p2,+(p2,p2)) -> +(p1,p5), +(p2,+(p2,+(p2,_0))) -> +(p1,+(p5,_0)), +(p5,p1) -> +(p1,p5), +(p5,+(p1,_0)) -> +(p1,+(p5,_0)), +(p5,p2) -> +(p2,p5), +(p5,+(p2,_0)) -> +(p2,+(p5,_0)), +(p5,+(p5,_0)) -> +(p10,_0), +(p10,p1) -> +(p1,p10), +(p10,+(p1,_0)) -> +(p1,+(p10,_0)), +(p10,p2) -> +(p2,p10), +(p10,+(p2,_0)) -> +(p2,+(p10,_0)), +(p10,p5) -> +(p5,p10), +(p10,+(p5,_0)) -> +(p5,+(p10,_0))} ## Trying with homeomorphic embeddings... Failed! ## Trying with polynomial interpretations... The constraints are satisfied by the polynomials: {p1:[0], +(_0,_1):[1 + _0 + _1], p5:[1], p2:[0], p10:[0], +^#(_0,_1):[_0]} for all instantiations of the variables with values greater than or equal to mu = 0. This DP problem is finite. ## DP problem: Dependency pairs = [+^#(p10,+(p5,_0)) -> +^#(p5,+(p10,_0)), +^#(p5,+(p5,_0)) -> +^#(p10,_0)] TRS = {+(p1,p1) -> p2, +(p1,+(p2,p2)) -> p5, +(p5,p5) -> p10, +(+(_0,_1),_2) -> +(_0,+(_1,_2)), +(p1,+(p1,_0)) -> +(p2,_0), +(p1,+(p2,+(p2,_0))) -> +(p5,_0), +(p2,p1) -> +(p1,p2), +(p2,+(p1,_0)) -> +(p1,+(p2,_0)), +(p2,+(p2,p2)) -> +(p1,p5), +(p2,+(p2,+(p2,_0))) -> +(p1,+(p5,_0)), +(p5,p1) -> +(p1,p5), +(p5,+(p1,_0)) -> +(p1,+(p5,_0)), +(p5,p2) -> +(p2,p5), +(p5,+(p2,_0)) -> +(p2,+(p5,_0)), +(p5,+(p5,_0)) -> +(p10,_0), +(p10,p1) -> +(p1,p10), +(p10,+(p1,_0)) -> +(p1,+(p10,_0)), +(p10,p2) -> +(p2,p10), +(p10,+(p2,_0)) -> +(p2,+(p10,_0)), +(p10,p5) -> +(p5,p10), +(p10,+(p5,_0)) -> +(p5,+(p10,_0))} ## Trying with homeomorphic embeddings... Failed! ## Trying with polynomial interpretations... The constraints are satisfied by the polynomials: {p1:[0], +(_0,_1):[1 + _0 + _1], p5:[1], p2:[0], p10:[0], +^#(_0,_1):[_0]} for all instantiations of the variables with values greater than or equal to mu = 0. This DP problem is finite. ## DP problem: Dependency pairs = [+^#(p10,+(p5,_0)) -> +^#(p5,+(p10,_0)), +^#(p5,+(p5,_0)) -> +^#(p10,_0)] TRS = {+(p1,p1) -> p2, +(p1,+(p2,p2)) -> p5, +(p5,p5) -> p10, +(+(_0,_1),_2) -> +(_0,+(_1,_2)), +(p1,+(p1,_0)) -> +(p2,_0), +(p1,+(p2,+(p2,_0))) -> +(p5,_0), +(p2,p1) -> +(p1,p2), +(p2,+(p1,_0)) -> +(p1,+(p2,_0)), +(p2,+(p2,p2)) -> +(p1,p5), +(p2,+(p2,+(p2,_0))) -> +(p1,+(p5,_0)), +(p5,p1) -> +(p1,p5), +(p5,+(p1,_0)) -> +(p1,+(p5,_0)), +(p5,p2) -> +(p2,p5), +(p5,+(p2,_0)) -> +(p2,+(p5,_0)), +(p5,+(p5,_0)) -> +(p10,_0), +(p10,p1) -> +(p1,p10), +(p10,+(p1,_0)) -> +(p1,+(p10,_0)), +(p10,p2) -> +(p2,p10), +(p10,+(p2,_0)) -> +(p2,+(p10,_0)), +(p10,p5) -> +(p5,p10), +(p10,+(p5,_0)) -> +(p5,+(p10,_0))} ## Trying with homeomorphic embeddings... Failed! ## Trying with polynomial interpretations... The constraints are satisfied by the polynomials: {p1:[0], +(_0,_1):[1 + _0 + _1], p5:[1], p2:[0], p10:[0], +^#(_0,_1):[_0]} for all instantiations of the variables with values greater than or equal to mu = 0. This DP problem is finite. ## DP problem: Dependency pairs = [+^#(p10,+(p5,_0)) -> +^#(p5,+(p10,_0)), +^#(p5,+(p5,_0)) -> +^#(p10,_0)] TRS = {+(p1,p1) -> p2, +(p1,+(p2,p2)) -> p5, +(p5,p5) -> p10, +(+(_0,_1),_2) -> +(_0,+(_1,_2)), +(p1,+(p1,_0)) -> +(p2,_0), +(p1,+(p2,+(p2,_0))) -> +(p5,_0), +(p2,p1) -> +(p1,p2), +(p2,+(p1,_0)) -> +(p1,+(p2,_0)), +(p2,+(p2,p2)) -> +(p1,p5), +(p2,+(p2,+(p2,_0))) -> +(p1,+(p5,_0)), +(p5,p1) -> +(p1,p5), +(p5,+(p1,_0)) -> +(p1,+(p5,_0)), +(p5,p2) -> +(p2,p5), +(p5,+(p2,_0)) -> +(p2,+(p5,_0)), +(p5,+(p5,_0)) -> +(p10,_0), +(p10,p1) -> +(p1,p10), +(p10,+(p1,_0)) -> +(p1,+(p10,_0)), +(p10,p2) -> +(p2,p10), +(p10,+(p2,_0)) -> +(p2,+(p10,_0)), +(p10,p5) -> +(p5,p10), +(p10,+(p5,_0)) -> +(p5,+(p10,_0))} ## Trying with homeomorphic embeddings... Failed! ## Trying with polynomial interpretations... The constraints are satisfied by the polynomials: {p1:[0], +(_0,_1):[1 + _0 + _1], p5:[1], p2:[0], p10:[0], +^#(_0,_1):[_0]} for all instantiations of the variables with values greater than or equal to mu = 0. This DP problem is finite. ## DP problem: Dependency pairs = [+^#(p1,+(p1,_0)) -> +^#(p2,_0), +^#(p2,+(p1,_0)) -> +^#(p1,+(p2,_0))] TRS = {+(p1,p1) -> p2, +(p1,+(p2,p2)) -> p5, +(p5,p5) -> p10, +(+(_0,_1),_2) -> +(_0,+(_1,_2)), +(p1,+(p1,_0)) -> +(p2,_0), +(p1,+(p2,+(p2,_0))) -> +(p5,_0), +(p2,p1) -> +(p1,p2), +(p2,+(p1,_0)) -> +(p1,+(p2,_0)), +(p2,+(p2,p2)) -> +(p1,p5), +(p2,+(p2,+(p2,_0))) -> +(p1,+(p5,_0)), +(p5,p1) -> +(p1,p5), +(p5,+(p1,_0)) -> +(p1,+(p5,_0)), +(p5,p2) -> +(p2,p5), +(p5,+(p2,_0)) -> +(p2,+(p5,_0)), +(p5,+(p5,_0)) -> +(p10,_0), +(p10,p1) -> +(p1,p10), +(p10,+(p1,_0)) -> +(p1,+(p10,_0)), +(p10,p2) -> +(p2,p10), +(p10,+(p2,_0)) -> +(p2,+(p10,_0)), +(p10,p5) -> +(p5,p10), +(p10,+(p5,_0)) -> +(p5,+(p10,_0))} ## Trying with homeomorphic embeddings... Failed! ## Trying with polynomial interpretations... The constraints are satisfied by the polynomials: {p1:[0], +(_0,_1):[2 + 2 * _0 + 2 * _1 + _0 * _1], p5:[0], p2:[1], p10:[0], +^#(_0,_1):[_0 + _1 + _0 * _1]} for all instantiations of the variables with values greater than or equal to mu = 0. This DP problem is finite. ## DP problem: Dependency pairs = [+^#(p1,+(p1,_0)) -> +^#(p2,_0), +^#(p2,+(p1,_0)) -> +^#(p1,+(p2,_0))] TRS = {+(p1,p1) -> p2, +(p1,+(p2,p2)) -> p5, +(p5,p5) -> p10, +(+(_0,_1),_2) -> +(_0,+(_1,_2)), +(p1,+(p1,_0)) -> +(p2,_0), +(p1,+(p2,+(p2,_0))) -> +(p5,_0), +(p2,p1) -> +(p1,p2), +(p2,+(p1,_0)) -> +(p1,+(p2,_0)), +(p2,+(p2,p2)) -> +(p1,p5), +(p2,+(p2,+(p2,_0))) -> +(p1,+(p5,_0)), +(p5,p1) -> +(p1,p5), +(p5,+(p1,_0)) -> +(p1,+(p5,_0)), +(p5,p2) -> +(p2,p5), +(p5,+(p2,_0)) -> +(p2,+(p5,_0)), +(p5,+(p5,_0)) -> +(p10,_0), +(p10,p1) -> +(p1,p10), +(p10,+(p1,_0)) -> +(p1,+(p10,_0)), +(p10,p2) -> +(p2,p10), +(p10,+(p2,_0)) -> +(p2,+(p10,_0)), +(p10,p5) -> +(p5,p10), +(p10,+(p5,_0)) -> +(p5,+(p10,_0))}
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